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Published: Mar 31 1758.
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Jac: Ferguson 4
ASTRONOMY
1
IN FIVE BOOKS.
BY
ROGER LONG, D.D. F. R. S
MASTER OF PEMBROKE HALL, AND LOWNDES'S
PROFESSOR OF ASTRONOMY AND GEOMETRY,
IN THE UNIVERSITY OF CAMBRIDGE.
VOL. II.
CAMBRIDGE,
PRINTED FOR THE AUTHOR,
M. DCC.LXIV.
Histo Sai
1.
Js a lo mog
12-2020
14-324-
(iii)
T
The frontispiece explained. The great ſphere at Pembroke Hall in
Cambridge
HE frontispiece to this volume is a print of what I call the Uranium,
becauſe it ſhews the heavenly bodies with their motions and appear-
ances in a more compleat manner than can be done by any other inftrument
that I know of; it confifts of a planetarium, or machine that exhibits the moti-
ons of the earth and all the primary planets round the fun, and the motion of
the moon round the earth all encloſed in a ſphere: upon the ſphere, beſides the
principal circles of the celeſtial globe, the zodiac is placed, of a breadth fuf-
ficient to contain the apparent path of the moon in all its deviations, with
all the ſtars over which the moon can ever país; as alfo the ecliptic, and the
heliocentric orbits of all the primary planets. The earth in the planetarium
has a moveable horizon to which a large moveable braſs circle marked bb
within the ſphere may be fet coincident, repreſenting the plane of the horizon
continued to the ſtarry heaven; the horizons being turned round fink below
the ſtars on the eaſt fide, and make them appear to riſe; and riſe above
the ſtars on the weft fide, and make them appear to fet: on the other hand,
the earth and the horizon being at reſt, the ſphere may be turned round to
repreſent the apparent diurnal motion of the heaven. The earth and planets in
the planetarium may be fet in their true places in their orbits for any day re-
quired, by an almanack; this being done, if we ſtretch a thread from the earth,
or imagin a line therefrom to be drawn through the fun, moon, and each pla-
net to the ſphere, it will mark the apparent places of them for that day: the
fun, moon and planets, repreſented by fmall beads of different colours, are
each of them put upon the end of a wire whereto a fpring is fixed, and may
thereby be put on the infide of the zodiac in their places before found; this
being done the ſphere turned round will fhew their apparent motions, their
rifing, fouthing, and ſetting for the day.
This ſphere may be made more compleat, if plates of tin or thin braſs be
hammered into fegments of a ſphere of the fame diameter, and upon the
concave fide of each plate one of the conftellations be drawn, and fixed in its
proper place: the ſuperfluous part of the plate ſhould be cut off, in order to
leave a clear view into the infide.
In purſuance of this idea, I have, in a room lately built in Pembroke
Hall, erected a ſphere of 18 feet diameter, wherein above thirty perſons may
*.
fit
(iv)
fit conveniently; the entrance into it is over the fouth pole by fix fteps: the
frame of the ſphere confiſts of a number of iron meridians, not compleat
femicircles, the northern ends of which are ſcrewed to a large round plate
of braſs with an hole in the center of it, through this hole from a beam in
the cieling comes the north pole, a round iron rod about 3 inches long, and
ſupports the upper part of the ſphere to its proper elevation for the latitude
of Cambridge; the lower part of the ſphere, fo much of it as is invifible in
England, is cut off; and the lower or fouthern ends of the meridians or
truncated femicircles terminate on, and are ſcrewed down to a ſtrong circle of
oak of about 13 feet diameter, which, when the ſphere is put into motion,
runs upon large rollers of lignum vitæ, in the manner that the tops of fome
wind-mills are made to turn round. Upon the iron meridians is fixed a zodiac of
tin painted blue, whereon the ecliptic and heliocentric orbits of the planets are
drawn, and the conftellations and ſtars traced: the great and little bear and
draco are already painted in their places round the north pole; the reſt of the
conſtellations are propoſed to follow: the whole is turned round with a ſmall
winch with as little labour as it takes to wind up a jack, though the weight
When it is made
of the iron, tin, and wooden circle is above 1000 pound.
uſe of, a planetarium will be placed in the middle thereof: the whole with
the floor is well fupported by a frame of large timber: the picture of the
Uranium makes it needlefs to give any farther defcription.
1
Subſcribers names which have come to hand fince the publication
of the first volume.
All Souls Coll. Library, Oxford.
Sir Robert Baylis Knt. Alderman of London.
Mr. Bentham of Cambridge.
Rev. Dr. Borlafe Vicar of Moddeves.
Francis Cholmondeley Eſq.
Rev. Dr. Cockman Mafter of Univerfity Coll. Ox.
Rev. Dr. Derham Prefident of St. Johns Oxford.
John Fuller of the Inner Temple Efq.
Nicholas Herbert Eq.
Rev. Mr. Heyter.
Rev. Dr. Huddesford Prefident of Trinity Coll. Ox.
Rev. Mr. John Jaumard.
Rev. Dr. Ifham Rector of Lincoln Coll. Oxford.
Rev. Dr. Mather Prefident of Corpus Chrifti Coll.
Oxford.
Mr. Melmoth.
Conyers Middleton D. D. Principal Librarian of
the University of Cambridge.
Rev. Dr. Niblett Warden of All Souls Coll. Oxford.
Mr. John Noon Bookfeller in London.
Rev. Dr. Panting Mafter of Pembroke Coll. Oxford.
Rev. Dr. Purnell Warden of New Coll. Oxford.
Rev. the Dean of Rapho.
The Right Hon. Earl Stanhope.
Rev. Mr. Shepherd Fellow of Chrift Coll. Plumian
Profeffor of Aftronomy and experimental Philofophy
in the University of Cambridge.
Rev. Dr. Shipman Fellow of All Souls Coll. Oxford.
Dr. Shippen Principal of Brazen Nofe Coll. Oxford.
Trinity Coll. Library, Oxford.
The Right Hon. Lady Charlotte Wentworth.
His Excellency General Wade.
page 357.
}
Book III.
D
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69
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e.
ASTRONOMY. BOOK III.
CHAP. I. OF THE SECONDARY PLANETS: THE MOON'S MOTION.
947 It has been mentioned before (pag. 189, §621) that three of the
primary planets, the earth, jupiter, and faturn are, in their revolutions
round the fun, attended by fecondary planets; theſe all go round their re-
ſpective primaries according to the order of the figns. The earth is attend-
ed only by the moon, which is uſually fignified by this character : the moon
goes round the earth, according to the order of the figns, at the diſtance
of about 60 femidiameters of the earth from the center of the earth, in a-
bout 27 days: which time is called a periodical month. The diſtances of the
fatellits of jupiter and faturn from their reſpective primaries and their pe-
riodical times will be fet down hereafter. In the 11th figure of the fecond
book, vol. 1. pag. 195, the very
ſmall circle upon the orbit of the earth at
the letter p repreſents the orbit of the moon: the four ſmall circles upon the
orbit of jupiter at the letter a are the orbits of jupiters four fatellits: the five
fmall circles upon the orbit of faturn near the character are the orbits of
the five fatellits of faturn; this figure is fufficient, for the prefent, to give the
reader a general idea of the orbits of the fecondary planets, though it does
not exhibit them in their true proportions; we ſhall proceed to greater ex-
actneſs in the fequel.
948 There is no certain diſcovery yet made of any other fecondary pla-
nets beſides thoſe mentioned in the foregoing ſection; but, from fome obſer-
vations made in the laſt century by Domenicho Caffini in Italy, and lately by
Mr. Short in London, it appears probable that the planet venus is attended
with at leaſt one fatellit. The account given us by Caffini is as follows",
a Decouverte de la lumiere celefte que paroift dans le zodiaque p. 45. ed Par,
Z z
'A. D. 1686
358
BOOK 3.
ASTRONOMY
'A. D. 1686 aug. the 28 at 15 minutes after 4 in the morning, looking at venus
'with a teleſcope of 34 feet, I faw, at the diftance of 3 of her diameter eaft-
333
'ward, a luminous appearance of a ſhape not well defined, that ſeemed to
'have the fame phafe with venus which was then gibbous on the weſtern
'fide. The diameter of this phenomenon was nearly equal to a 4th part of
'the diameter of venus. I obferved it attentively for a quarter of an hour, and,
'having left off looking at it for 4 or 5 minutes, I faw it no more: but day-
'light was then advanced. I had ſeen a like phenomenon which reſembled
'the phaſe of venus, jan. 25 A.D. 1672 from 52 minutes after 6 in the morn-
'ing to 2 minutes after 7, when the brightneſs of the twilight cauſed it to
'diſappear. Venus was then horned, and this phenomenon the diameter
'whereof was nearly a 4th part of the diameter of venus was of the ſame
'fhape. It was diſtant from the fouthern horn of venus a diameter of venus
'on the weſtern fide. In theſe two obfervations, I was in doubt whether it
'were not a fatellit of venus, of fuch a confiftance as not to be very well fitted
"to reflect the light of the fun, and which in magnitude bore nearly the fame
'proportion to venus as the moon does to the earth, being at the fame diſtance
'from the fun and the earth as venus was, the phaſes whereof it reſembled.
"Notwithſtanding all the pains I took in looking for it, after theſe two obſerva-
'tions, and at divers other times, in order to compleat fo confiderable a dif-
"covery, I was never able to fee it any more than theſe two times; I therefore
'fufpend my judgment of this phenomenon. If it fhould return often, there
'will be theſe two epochas which compared with other obſervations may be
'of uſe to find out the periodical time of its return, if it can be reduced to
"any rule.
949 Oct. 23, 1740, at funrife, Mr. Short, with a reflecting teleſcope of
16.5 inches which magnified about 50 or 60 times, perceived a ſmall ſtar at
about the diſtance of 10 from venus, as meaſured by the micrometer: and,
putting on a magnifying power of 240 times, he found the ftar put on the
phaſe of venus: he tried another magnifying power of 140 times, and even
then found the ftar have the fame phaſe: its diameter ſeemed about a third
or fomewhat lefs of the diameter of venus, its light was not fo bright or vi-
vid, but exceedingly ſharp and well defined: a line paffing through the center
of venus and it made an angle with the equator of about 18 or 20 degrees:
he faw it for the ſpace of an hour ſeveral times that morning; but, the light
of the fun increaſing, he loft it about a quarter of an hour after eight. He
fays, he looked for it every clear morning after this, but never faw it againa.
a Philoſ. tranſact. n. 459 for the months jan. feb. march 1748
950
Book III.
70
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CHAP. I.
359
ASTRONOMY
950 If we imagin the plane of the orbit of the moon to be extended to FIG.
the ſphere of the heaven, it would mark thereon a great circle, which may
be called the moon's apparent orbita; becauſe the moon appears to the inhabi-
tants of the earth to go in that circle through the 12 figns of the zodiac in a
periodical month: thus fig. 1, let EFGHI be the orbit of the earth, s the fun, I
abcd the orbit of the moon, when the earth is at E: let ABCD be a great cir-
cle in the ſphere of the heaven in the fame plane with the moon's orbit; the
moon, by going round her orbit abcd according to the order of the letters,
appears to an inhabitant of the earth to go round in the great circle ABCD,
according to the order of thofe letters: for when the moon is at a ſeen from
E fhe appears at A: when the moon is got to b fhe appears at B: when to c
ſhe will appear at c: when arrived at d ſhe will appear at D. It is true when
the moon is at b the viſual line drawn from E through the moon terminates
in L; as it does in м when the moon is at d: but the lines LM and DB, being
parallel, and not farther diſtant from each other than the diameter of the
earth's orbit, are as to ſenſe coincident, their diſtance meaſured in the ſphere
of the heaven is infenfible. For the fame reaſon, though the earth moves from
E to F in the time that the moon goes round her orbit, ſo that at the end of a
periodical month the moon will be at a, and is feen from the earth at F in the
line FN, the moon will notwithſtanding appear at A; the lines F N and E A
being parallel, and as to fenfe coincident. In like manner, whatever part
of her orbit the earth is in, as at H or 1, the moon, by going round in her orbit,
will appear to an inhabitant of the earth to go round in the great circle ABCD.
951 The orbit of every fecondary planet is an ellipfis having its primary in
one of its focuſes: if we confider the ellipfis in the ſecond figure as the orbit 2
of the moon; the greater axis AP is called the line of the moon's apfides: the
point p where the moon approaches neareſt to the earth fituated in the focus
E is the moon's perigee, or lower apfis: the point a where ſhe is at the greateſt
diſtance from the earth is the moon's apogee, or higher apfis: the extream points
of the leffer axis м and m are the places where the moon is at her mean or
middle diſtance from the earth; and a line drawn from the earth to either of
theſe points, as EM, or Em, is the line of the moon's mean diſtance: the di-
ſtance of either focus E or F from the center c is the excentricity of the moon's
orbit: If we imagine the mean diſtance of the moon to be divided into 1000
a Aftronomers, when they mention the orbit of the moon, fometimes mean the moon's real orbit, or
the curve wherein ſhe goes round the earth, which is deſcribed § 947; fometimes they mean the apparent
orbit of the moon: a little attention will make it eaſy to find which of theſe two is to be underſtood in any
writer.
Zz2
equal
360
воок 3.
ASTRONOMY
FIG. equal parts, the meanª excentricity of the moon is about 55
The
of thefe parts.
orbits of the fatellits of jupiter and faturn differ but little from circles.
952 The motion of every fecondary planet is not equable, but according to
this law, that a line drawn from the primary planet to its fecondary moves.
over equal areas upon the plane of the fecondary's orbit in equal times: The
moon's motion is therefore fwifteft in perigee, floweft in apogee, mean at
3 her mean diſtances; fee § 672: thus, fig. 3, let the orbit of the moon be re-
prefented by the ellipfis Am PM, let E be the focus thereof in which the earth
is fituated, if lines be drawn from E fo as to divide the area of it into equal
triangles, the unequal arcs will ſhew the inequality of the moon's motion: for
the moon will in the fame time go through the arc Pa as through the arc ab
or bм or мc or cd, &c. The orbits of the fatellits of jupiter and faturn being
but little different from circles, the motion of thoſe fatellits is nearly equable.
953 The planes of the orbits of the fecondary planets are not coincident with
the planes of the orbits of their primaries, but inclined to them: The plane
of the moon's orbit is inclined to the plane of the orbit of the earth in an an-
gle of about 5 degrees.-The inclinations of the planes of the orbits of the
fatellits of jupiter and faturn will be given hereafter.
་
954 The orbit of every fecondary planet would continue always invariably
the fame both as to its excentricity, the pofition of its longeſt axis, and
the fituation of its plane, if it were not diſturbed by any other of the hea-
venly bodies; in the fame manner as the orbits of the primary planets were
faid to continue invariable, § 794; though the planets perhaps may be liable
to be a little diſturbed by one another, or by the near approach of comets,
fo as to cauſe ſome change in their orbits. If the plane of the moon's orbit
were to continue invariable, and always parallel to it ſelf, fhe would always
appear to deſcribe the fame great circle in the fphere of the fixt ftars; and thoſe
points in that circle wherein the appears at her greateſt, leaſt or mean diſtan-
4 ces from the earth would always be the fame: in fig. 4. let ABCD be the orbit
of the earth in a perſpective view, the ecliptic, abcd the moon's orbit
which ſhe goes in when the earth is at A: let her orbit be efgh when the
earth is at B; let it be iklm when the earth at c, and nopq when the earth
is at D: if the plane of the moon's orbit, in every one of theſe places A, B, C,
and D, and in all the intermediate points of the earth's orbit, were to conti-
nue parallel to it felf, there would indeed be fo many different planes, but,
continued to the heaven, they would all mark the fame great circle thereon,
which is expreſt in the figure by the dotted line; for though the diſtance be-
a I mention here the mean excentricity, becauſe the moon's excentricity is variable, as we ſhall fee
hereafter.
tween
CHAP. I.
361
ASTRONOMY
tween the plane abcd and the plane iklm if both were extended would be FIG.
confiderable in it ſelf, it becomes infenfible in the ſphere of the fixt ſtars: In
like manner, if the longeſt axis of the moon's elliptic orbit continued always
parallel to it ſelf, and if the place of the apogee were in the point as it is
drawn in the 4th figure, the moon would always appear in apogee when in
4
, in perigee when in b, in her mean diſtance when in r or ≈.
955 The plane of the moon's orbit extended to the heaven cuts the eclip
tic in two oppofite points, confequently the moon's apparent orbit cuts the
ecliptic in two oppofite points. The two points where the moon's apparent
orbit cuts the ecliptic are called the moon's nodes: the point where the moon
appears to croſs the ecliptic as fhe goes into north latitude is called the moon's
afcending node, of which this is the character : the point where the moon
croffes the ecliptic going into fouth latitude is her defcending node, marked
thus : the moon's afcending node is often called the dragon's head; her de-
ſcending node the dragon's tail: fome writers call the moon's apparent or-
bit her dragon: thefe appellations owe their origin to the repreſenting the
apparent orbit of the moon and the ecliptic as in fig. 5, which has fome 5
reſemblance of two ſnakes joyned together at their heads and tails; in this
view, the Arabians call thoſe parts of the moon's circle where ſhe is at the
greateſt diſtance from the ecliptic, as about L and 7, the dragon's bellies. By
a dragon the ancients meant a large fnake, not fuch a fictitious animal with
wings as the painters give us. The line of the moon's nodes is a line drawn from
one node to the other. The moon appears in the ecliptic only when ſhe is
in one of her nodes, in all other parts of her apparent orbit fhe is in north or
fouth latitude: thus if we ſuppoſe the moon, fig. 4, to be this day in her a 4-
fcending node in v, whilſt ſhe is going the first quarter of her revolution ſhe
appears to deviate gradually more and more northward from the ecliptic, till
ſhe is got to her utmoſt north latitude or limit at n, where her latitude is
about 5°: from her north limit her latitude gradually decreaſes, till ſhe comes
into the ecliptic at her defcending node in: from thence the deviates in
like manner fouthward from the ecliptic, till the is in her utmoſt ſouth lati-
tude or limit at s, where alſo her latitude is about 5°: from her ſouth limit
the continually draws nearer to the ecliptic, till fhe returns to her aſcending
node in . All this is eafily underſtood by fig. 4, which repreſents the zo- 4
diac in a perſpective view, the black circle drawn through the middle of the
zodiac and marked with the characters of the 12 figns 8 &c is the e-
cliptic; the dotted circle with 2 and & and n, s, the moon's north and
fouth. limits marked upon it is the moon's apparent orbit.
956
362
BOOK 3.
ASTRONOMY
FIG.
956 When the moon's place in which ſhe appears to an inhabitant of the
earth is the fame with the fun's place, the moon is faid to be in conjunction:
when the moon's place is oppofite to the fun's place, ſhe is ſaid to be in oppo-
fition: when the moon is a quarter of a circle diſtant from the fun, ſhe is ſaid
to be in quadrature: an exact or central conjunction or oppofition can only fall
out when the moon is in the ecliptic, but it is called a conjunction when the
moon is in the ſame femicircle of a fecondary of the ecliptic with the fun,
though the moon has then latitude: this remark is applicable alſo to the op-
4 pofition and quadrature: thus fig. 4, fuppofe the moon to appear in the point
r, if the fun be there alfo it is a central conjunction: if the moon appears
in v when the fun is at, it is a central oppofition: if the fun be at or
when the moon appears in √, it is a quadrature ſtrictly fo: but it is call-
ed a conjunction, if the moon be at n the fun at : an oppofition, if the
moon be at n the fun at b: a quadrature, if the moon be at n the fun at v
or. Both conjunction and oppofition of the moon are called fyzygies: the
word in the original σuçuya properly fignifies conjunction, but may well
enough take in the moon's oppofition; for then alſo the fun moon and earth
may be faid to be conjoyned, by a line which paffes through them all three:
the uſe of this term will fave the tedious repetition of conjunction and oppo-
fition, when the fun's action upon the moon comes to be treated of. A line
drawn through the points of oppofition and conjunction is called the line of
fyzygies.
957 The common lunar month, or the time which paffes between any con-
junction and the conjunction immediately following, is called a fynodical month,
or a lunation: in this time, the moon, by turning more or lefs of her enlight-
ned hemifphere towards our earth, goes through all the differences of her
increaſe and waining: from her conjunction to the next oppofition the moon
is faid to be in her increaſe, becauſe ſhe then fhews us every day more and
more of her enlightned hemiſphere; appearing firſt a new moon, then a cre-
Scent, an half moon, gibbous, a full moon: from oppofition to the next con-
junction the moon is in the wain; and, turning every day leſs and leſs of her
enlightned hemifphere towards the earth, appears in the fame fhapes over
again as before, but inverted, and in an inverted order: thefe feveral ap-
pearances are called the phases of the moon; an explanation of them ſhall be
given in the next chapter: the word phaſe, pars, fignifies an appearance.
958 The moon's motion in her apparent orbit is confidered either abſo-
lutely, or with relation to the fun: the moon's motion confidered abfolutely is
fometimes ſwifter than at other times, according as ſhe is nearer to her peri-
gee, where ſhe is ſwifteft, or to her apogee, where floweft; as was ſaid § 952:
the
>
CHAP. r.
363
ASTRONOMY
the moon's mean motion is at the rate of 13° 10′ 35″ in a day, which carries FIG.
her round the zodiac and compleats the periodical month in 27d7h43. The
moon's motion with relation to the fun is called her motion from the fun, or
her elongation from the fun: the moon's motion from the fun is the excefs of
the velocity of the moon's motion in her apparent orbit above the velocity of
the fun's apparent motion in the ecliptic: this excefs is fometimes greater
than at other times, for two reaſons; 1, from the inequality of the moon's
motion, § 952; 2, from the inequality of the fun's motion, § 776: the mean
motion of the moon from the fun is 12° 11′ 27″ in a day, which carries the moon
from one conjunction to another, and finiſhes the fynodical month in 29d 12h.
44. The mean motion of the fun in the ecliptic being 59′ 8″ in a day, and
the mean motion of the moon in her apparent orbit 13°10′ 35″ in a day; the
moon's apparent motion in the zodiac is 12° 11′ 27″ fafter than that of the fun..
959 If the earth had no revolution round the fun, the periodical and ſy-
nodical month would be the fame; the greater length of the fynodical is ow-
ing to the fun's apparent motion in the ecliptic, which is cauſed by the earth's
motion in her orbit, as was fhewn § 642, by reaſon whereof about two days
more than a periodical month will pafs from the time that the moon is in
any given fituation with regard to the fun to the time when ſhe will be a-
gain in the like fituation, and ſhew us again the fame phaſe: thus, fig. 4, 4
ſuppoſe the moon is this day at noon in conjunction with the fun in the point
r; in a periodical month of 27d7h43′ the moon will perform a revolution
in her orbit, and appear again in conjunction with the point ; but the fun
in that time will
appear to have gone almoft 27° from r; and there cannot
be another conjunction till the moon has overtaken the fun, which will not
be till about two days more have paffed, when the fun and moon will be
both in about the 29° of V; the fun being then at a the moon at b.
960 The moon, being nearer to the earth than any other of the heavenly
bodies, may come between our eye and any of them that is in or near the e-
cliptic: when the moon in her motion along the zodiac appears with one
edge of her diſk firſt to touch a ſtar, it is called an appulfe of the moon to that
ſtar; and during the time the ſtar is hid from our view by the interpofition
of the moon there is faid to be an occultation of it: the beginning of an occul-
tation is beft obferved when that fide of the moon which firſt touches the
ftar is dark; the end of an occultation is beſt obſerved when it is a dark fide
of the moon's difk which laſt leaves the ftar in paffing over it what is here
ſaid of the occultations of ftars by the moon or appulfes of the moon to them>
is applicable alſo to the planets; there is however this difference, that, the
apparent diameters of the fixt ſtars being infenfible, a ſtar is hid from our
view.
1
364
BOOK 3.
ASTRONOMY
EIG. view the moment the moon appears to touch it; whereas the diſk of a pla-
net, being of a fenfible magnitude, is not covered by the moon all at once, but,
as the moon's diſk gradually hides more and more of it, appears leſs and leſs,
till the part not yet covered by the moon is too ſmall to be vifible with the
teleſcope we make uſe of: and confequently the more the teleſcope magni-
fies, the longer will the time be between the moment of the firſt appulſe of
the moon to a planet and that of the planet being totally hid from the obſer-
ver by the moon.
4
961 Hitherto the orbit of the moon has been confidered as invariable, as it
would be if there were no other bodies befides the earth and the moon in the
univerſe, or none near enough to affect either of them in a ſenſible manner:
the fun has an influence upon both thoſe bodies; and, as the moon in her
-revolution round the earth is fometimes nearer the fun than at other times,
he is variouſly diſturbed by him in that revolution; having her motion fome-
times accelerated, and at other times retarded, ſo as to be hindered thereby
from defcribing equal areas in equal times round the earth: ſuffering alſo va-
rious changes in the curvature of her orbit, and in the poſition of the plane
thereof: all theſe changes will be better accounted for when the cauſes of the
planetary motions have been explained; it is however neceffary at preſent to
take fome notice of two of them, the first is, that the moon's apogee, and
confequently her perigee and the places of her mean diſtances have a flow
motion, which carries them round the zodiac, according to the order of the
figns, in about 9 years: the fecond, that the nodes of the moon have a flow
retrograde motion, ſo as to go round the ecliptic, contrary to the order of the
figns, in 19 years.
:
962 In order to fhew the progreffion of the moon's apogee, in fig. 4, let
√ns repreſent the apparent orbit of the moon, ABCD the orbit of the
earth, the ſmall black ellipfes round the earth at theſe ſeveral letters the or-
-bit of the moon, when the earth is in thoſe ſeveral fituations: when the earth
is at A let the apogee of the moon be at d, the place of the moon's apogee
in the ſphere of the heaven will then be the point, and if bd the longeft
axis of the moon's ellipfis were to continue parallel to it ſelf, and confequent-
ly to the line, when the earth is in every other point of her orbit, for
example, at B, or.c, or D, as that axis is drawn at hf, m k, and q o, the place
of the moon's apogee in the ſphere of the heaven would be always the fame,
namely at, becauſe all parallel lines which are no farther diſtant from each
other than the diameter of the earth's orbit are in effect coincident, or appear
to terminate in the fame point of the heaven: but this is not the cafe, for the
moon's apogee is carried forward, in ſuch a manner, that in a years. time when
the
CHAP. 2.
365
ASTRONOMY
•
the earth ſhall have gone round the circle ABCD and is returned again to FIG.
the point A, the moon's orbit will be in the fituation repreſented by the dot- 4
ted ellipfis, the longeſt axis whereof will not be bd but rt: parallel to, and
confequently as to fenfe coincident with EF, and the place of the moon's
apogee will then be at F, which will be about the middle of a.
963 In order to exhibit the going back of the moon's nodes, it must be ob-
ſerved that the plane of the moon's orbit does not continue parallel to it
felf, and confequently, if we fuppofe it extended to the ſphere of the heaven,
would not mark always the fame circle thereon, as was reprefented fig. 4 but
changes its fituation in ſuch a manner that, fuppofing at the beginning of a
month the fituation of it were fuch that extended to the heaven it would
mark thereon the circle ABCD fig. 6, in which the moon's aſcending node 6
is r, the deſcending; at the end of the month when the moon has gone
round the zodiac and is returned to r, the plane of her orbit will be fo fitu-
ated that extended to the ſphere of the heaven it would then mark thereon
the daſhed circle EFGH, in which the aſcending node of the moon is at a
about the 28 degree of , the deſcending node at b about the 28° of "; or,
to ſhew it ſtill more accurately, it may be repreſented by the 7th figure which
7
is a perſpective view of the zodiac, wherein the pointed line markes the eclip-
tic, and the black line that croffes it obliquely fhews how the moon ſeen
from the earth does not defcribe in the ſphere of the heaven a circle return-
ing into it ſelf, but a curve returning into the ecliptic twice in every revolu-
tion of the moon, not exactly in the ſame points where it croffed the eclip-
tic before, but a little diſtant from thoſe points, backward, or contrary to
the order of the figns: thus, in the figure before us, if at the beginning of
one periodical month the moon's afcending node was a, at the beginning of
the next it would be b, at the beginning of the next, c, &c: in like manner
the deſcending node changes its place, as may be feen in the figure.
CHAP. 2. THAT THE SECONDARY PLANETS ARE OPAKE BODIES AND
BORROW ALL THEIR LIGHT FROM THE SUN.
964 The ſecondary planets are fpherical opake rough bodies, and appear
luminous only on that part of them which receives light from the fun and
reflects it to us: the fun, by reaſon of his great diſtance, though much larger
than any fecondary planet, can illuminate only one half or not fenfibly more
than one half of its furface at a time, if that furface were perfectly fmooth
like a poliſhed globe, the planet would be invifible, as was faid of the prima-
ries, § 722.
965
3 A
366
воок 3.
ASTRONOMY
965 The moon being a globular opake body of a rough ſurface, every part
of it upon which the light of the fun falls reflects it every way: ſome parts
of the moon are better fitted to reflect the light of the fun than others: the
dark parts are by fome philofophers thought to be feas and lakes; becauſe
the line which divides the part of the moon which is illuminated by the fun
from that which is not fo is not jagged and uneven where it paffes over thoſe
dark ſpots, as it is where it paffes over the brighter parts of the moon, that
are ſuppoſed to be land diverfified with hills and valleys. It is faid indeed that
a good teleſcope will diſcover in the darkeſt parts of the moon caverns and
empty pits, and that theſe cannot be in a liquid body, Keil lect. 10: but
not the lunar feas and lakes have iſlands in them wherein there
may be pits
and caverns? and, if fome of theſe dark parts are brighter than others, may
not that be owing to the feas and lakes being of different depths, and to their
having rocks in fome places, and flats in others?
may
966 The furface of the moon is not only rough, but there are alſo upon
it very high mountains, and deep valleys: if the furface of the moon were
even, none of its parts prominent above the reft, the illuminated. part would
be divided from the dark, in the half moon, by an even ſtrait line, and, in
all other phaſes, by an even elliptic line; whereas, if we view the moon
through a teleſcope, we find no regular line ſeparating light and darkneſs
up-
on her furface; but the confines between them are very irregular, and as it
were indented, with innumerable breaks: and even in the dark part of the
moon, near the lucid ſurface, are ſeen ſome ſmall places exceedingly bright,
that ſeem to ſtand out and be detached from the body of the moon: theſe are
no other than the tops of mountains and rocks, that, by reaſon of their height,
are illuminated by the fun, when he is in fuch a fituation that his light can-
not reach their lower parts, nor thoſe places on the ſurface of the moon up-
on which theſe rocks or mountains ſtand.
There are alſo obſer-
vable upon the illuminated part of the moon ſeveral darkiſk ſpots, that by
the teleſcope are plainly diſcovered to be deep cavities, furrounded with hills
that caſt a ſhadow into them: for this ſhadow is caft on different fides of the ·
cavities, according as the fun is in different pofitions, in the increaſe or wain
of the moon, but at the full moon, when the fun's rays are perpendicular to
the bottom of the cavities, no fhadow is ſeen therein.
967 The moon going round our earth in a much leſs orbit than the earth
revolves in round the fun, fometimes more fometimes lefs and ſometimes no
part of her enlightened half will be towards us: and this is the cauſe of the
different phaſes of the moon before mentioned § 957. If a ſmall globe be
one half black and the other white, by turning it flowly round, we may ex-
hibit
page 367.
Book III.
1
K
C
L
C
M
m
N
9
P
I
H
k
8
h
G
9
a
A
B
F
d
D
E
71
10
11
W. J. **.
HOI
UNIV
CHAP. 2.
367
ASTRONOMY
hibit all the phaſes of the moon, from the new moon to the full, and from FIG.
the full to the laſt phaſe in which the moon appears juſt before her approach-
ing ſo near conjunction with the fun as to be invifible. How theſe feveral
phaſes ariſe from the different fituation of the moon in reſpect of the ſun
and the earth may alſo be eaſily underſtood by the following figure, fig. 8, 8
let s be the fun, E the earth, let abcde &c be the orbit of the moon;
when the moon is at a in conjunction with the fun the whole dark hemi-
ſphere of her is towards the earth, ſhe is therefore at that time inviſible to
us: when the moon is gone from a to b a ſmall part of her enlightened hemi-
ſphere will be turned towards the earth, and the then appears as at B: as ſhe
goes on in her orbit according to the order of the letters, more and more of
her enlightened hemiſphere is turned towards our earth, ſo that at c fhe
pears as at c, at d as at D; when the moon is at e half her enlightened and
half her dark hemiſphere is turned towards our earth, and the appears as at
E: thus the moon turns daily more and more of her enlightened hemiſphere
towards the earth, ſo that at ƒ fhe appears as at F, at g as at G, at h as at н,
till at i her whole enlightened hemifphere is turned towards the earth, and
ſhe appears a full-moon, as at 1: from thence, at k, l, m, n, &c ſhe turns e-
very day leſs and leſs of her enlightened hemiſphere towards the earth, and
appears as at K, L, M, N, &c ſhewing us fucceffively the fame phaſes as be-
fore, but inverted, and in an inverted order, till fhe arrives at the next con-
junction at a, and is again inviſible.
1
ap-
968 When the moon is in quadrature with the fun at E and fhews us half
her enlightened and half her dark hemiſphere, ſhe is ſaid to be in dichotomy,
or to be bisected; this phaſe of the moon is of all others the moſt eaſy to find
the exact time of, by two obfervations of the line that divides the bright part
of the moon from the dark; one before the dichotomy, when the line from
being bent begins to appear ſtrait; the other after the dichotomy, when that
line from being ſtrait begins to appear bent; the middle time between theſe
two obſervations is the moment of dichotomy. The time of the exact full
moon is not ſo eafily found by the phaſes, becauſe there is no ſenſible diffe-
rence in the phaſe of the moon for a confiderable time when at the full.
969 To a ſpectator placed upon the moon our earth would, every month,
fhew all the ſeveral phaſes of the moon: thus, fig. 8, when the moon is at 8
¿ only the dark half of the earth is turned towards the moon, and confequent-
ly the earth would there be invifible: when the moon is at k a ſmall part of
the enlightened half of the earth is turned towards the moon, and would ſhew
a ſpectator there the fame appearance as a new moon is to us: and as the
moon goes on according to the order of the letters k, l, m, n, &c, more and
3 A 2
more
368
воок 3.
ASTRONOM Y
FIG. more of the enlightened half of the earth is turned towards the moon, and
would exhibit to a fpectator there the phaſes of an increating moon, till the
moon is arrived at a, where the earth would appear as a full moon; from
thence, as the moon goes round according to the order of the letters a b c d
&c, the earth would fhew all the phaſes of the waining moon, till the moon
is arrived again at i, where the earth, being again in conjunction with the
fun in reſpect of a ſpectator placed upon the moon, would be again inviſible
to him. The earth being much larger than the moon, the diſk of the earth
would appear much larger to a ſpectator upon the moon than the moon does
to us; and confequently, if the earth and the moon are equally fitted to re-
flect the light of the fun, the earth throws a much greater quantity of light
upon the moon than the moon does upon the earth.
970 For a few days before and after conjunction with the fun, as when
8 the moon is at a, b, c, d, or q, fig. 8, the dark part of the moon's diſk is not
perfectly dark, if it were fo, it would be quite invifible to us: that obſcure
light which makes it then feen by us is reflected upon it from the enlight-
ened half of the earth, which is at thoſe times turned moſt directly towards
the dark fide of the moon: in all other fituations, as e, f, g, h, m, n, o, p, ſo
much of the dark half of the earth is turned towards the moon that ſhe receives
very little light from the earth, or is in fuch a poſition that a great deal of
what ſhe does receive from thence is not reflected towards the earth, but is
ſcattered into the ſpace which furrounds the earth: add to this, that the
more we have of the illuminated half of the moon turned towards our earth
the larger is the luminous object which the moon prefents to our view; and
confequently, the weaker impreffion will the faint light of the obſcure part
of the moon make upon the eye: in theſe caſes, only the bright part of the
moon which is immediately enlightened by the fun is viſible to us.
When the moon is in conjunction with the fun or very nearly ſo ſhe is in-
viſible, though, in that fituation, the illuminated half of the earth is moſt
directly turned towards the dark part of the moon, and throws the greateſt
quantity of light thereon: this is owing to the nearneſs of the fun, whoſe ſu-
perior brightneſs prevents the weaker light not only of the moon, but that
of the ſtars and planets alfo, from being feen, when very near him. It may
be obferved in general, that, whenever an object makes a very ſtrong impref-
fion
upon any of our fenfes, any other object which at the fame time ftrikes
but faintly upon the ſame ſenſe will be quite imperceptible.
971 To a fpectator placed upon jupiter or faturn every fatellit of the pla-
net upon which he ſtands would, in the periodical time of its revolution round
its primary, appear to go through all the phaſes of the moon: this is eafily feen
by
CHAP. 3.
369
ASTRONOMY
·
by the eighth figure; if we fuppofe s to be the fun, E jupiter or faturn, and FIG.
abcde &c the orbit of a fatellit of one of thofe primary planets.
8
972 The diſtance of any fatellit of jupiter or faturn from its primary is in-
confiderable, if compared with the diſtance of the primary from the fun; the
fatellits therefore of thoſe planets are illuminated by the fun very nearly in the
fame manner as their refpective primaries are: the diftance of any fatellit of
jupiter or faturn from its primary is alſo inconfiderable, if compared with the
diftance of the primary from the earth: every fatellit therefore of jupiter or
faturn, ſeen from our earth, muſt always appear near its primary; and con-
fequently, like its primary, turns much the greatest part of its enlightened
half towards the earth, and to us muſt always appear round, as thofe prima-
ry planets do; fee § 726: indeed thoſe fatellits are fo fmall, and their diſtance
from us fo great, that, if they were to turn towards us the feveral phaſes of
the moon, the beſt teleſcopes would hardly diſcover any difference in their
ſhapes, though they might fhew them perhaps fometimes a little larger or
brighter than at other times.
CHAP. 3. OF ECLIPSES OF THE MOON.
973 We come now to treat of the defects or eclipſes of the luminaries; ap-
pearances that in old time were beheld with terror and amazement, as pro-
digies that portended great and various calamities to mankind: but when it
came to be diſcovered that they arife from natural caufes, and that the times
of their falling out may be foretold long before they happen by the fkilful
in aſtronomy, it gave great reputation to that fcience: not only as theſe pre-
dictions demonftrate the certainty of it, but as they ſerve to deliver mankind,
at leaſt the wiſer part, from thofe fuperftitious apprehenfions with which
they uſed to be difmayed. Thefe confiderations induced a learned heathen
to admire the fagacity of thoſe who were able, as he phrafes it, to find out
the laws which fuch great deities as the fun and moon obſerve, and made him
run out in their praiſes, as perfons of an elevated genius, who had attained
to fomething above the capacity of human nature a
974 The word eclipſe, exλerfis, is derived from a greek word that figni-
fies to be diminiſhed or deficient, to faint away, to ſwoon, or to dye: when
the full moon in her greateſt luftre falls into the fhadow of the earth, and is
deprived of the enlivening beams of the fun, the appears pale and languid be-
fore her obſcuration, as if the were fick and going to dye: from hence, the
a v. Plin. nat hift. 1. 2. c. 9, & 12.
ignorant
370
ASTRONOMY
BOOK 3.
ignorant heathen imagined the moon was in pain at thoſe times, and there-
fore lunar eclipſes were called by them luna labores, the ſtruggles or agonies
of the moon; and, in order to relieve her in that fancied diſtreſs, they uſed
to hold up on high lighted torches, to keep blowing with trumpets and horns,
and to make a clattering upon veffels of braſs and iron, and to facrifice to the
moon after the eclipfe was over: this practice we find to be of great antiqui-
ty, as well as the opinion that it was in the power of witches by their ſpells
and charms not only to darken the moon, but to bring her down from her
orb, and force her to ſhed baleful influences upon the earth ª
975 The fun alſo, when the moon comes between him and our earth, and
deprives us of his light and heat, appears to us dark or deficient, and was,
eſpecially when he was totally eclipſed, by many of the ancients thought to
turn away his face, in abhorrence of fome atrocious crime that had been, or
was about to be perpetrated in the earth, and to threaten mankind with ever-
lafting night, and the death or deftruction of the world b.
The Chineſe, who have, for above 2000 years before the incarnation of
our Saviour, been conſtant obſervers of eclipfes, though they did not take
much notice of thoſe of the moon, looked upon eclipſes of the fun in general
as unfortunate, but thoſe which fell out upon the first day of the year they
thought more particularly foreboded misfortunes to befall their Emperor,
who on fuch occafions did not receive the complements uſually paid him on
the beginning of the new year. When an eclipfe of the fun was expected, from
the predictions of their aftronomers, they made preparation at court for the
obfervation of it: as foon as it was begun, a blind man beat a drum, upon
which we are told the Mandarins or great officers mounted their horſes, and
there was a concourfe of people, I ſuppoſe near the court: if an eclipſe did
not happen at the time foretold, for they were not very certain in their cal-
culations, they congratulated the Emperor upon it; as they did alſo if the
obfcuration of the fun was leſs than was expected, or if clouds hindered the
eclipſe being viſible: when the eclipſe was over they offered ſacrifice.
976 The uſe of eclipfes in aſtronomy, geography, and chronology, will
be taken notice of hereafter, it is not amifs in the mean time, with Ricciolus
1. 5. c. 2. to mention the tendency they naturally had to draw off the heathen
from that idolatrous worſhip which they paid to the fun and moon: the Ynca
of Peru, mentioned by Garcilaso de la Vega in his R. commentàries of Peru,
9. c. 10, reaſoned very juftly, when he concluded that the fun could not
1.
5.
. c. 2.
a Veteres fcriptores, prefertim poeta et hiftorici, paſſim. v. quos citat Ricciolus, 7. 5. c. 1.
b v. Plin. nat. hift. I. 2. c. 12. et que ibi annotavit Dalecampius. v. etiam Ricciol. I.
c Gaubil Hiftoire, et traite de l'aftronomie Chinoife, vol. 2. p. 140. et vol. 3. p. 241. &c.
be
page 371.
A
S
Book III.
S
S
12
13
14
氮
​B
I
P
H
E
C
A
E
F
P
G
D
H
A
-F
B
C
D
T
P
A
H
M
S
15
E
N
W. Stephens fc.
L
B
Q
72
V
G
но,
CHAP. 3.
371
ASTRONOMY
be a divine being, becauſe he could obferve in him no token of freedom or will,
but that he went on neceffarily and invariably always in the fame courfe, as if
under the direction of another: ought not men to have degraded the fun and
moon from their fancied divinity, when they fo often faw them to be wholly
or in part deprived of their light, or hindered from ſending it upon the earth?
977 Something has already been faid, § 947, about the diſtance of the
moon from the earth, and that this diſtance is variable, § 951. It will be pro-
per
before we enter upon eclipſes of the moon to fhew by what methods we
come to the knowledge of theſe things. The horizontal parallax of the moon
being found, her diſtance from the center of the earth may be known by §
147. There are ſeveral ways of finding the horizontal parallax of the moon,
which may be ſeen in Ricciolus, Tacquet, Keil, &c. I fhall give a ſhort ac-
count of two of them. The firft is from Ptolemy's Almageft . 5. c. 13.
៖
978 Ptolemy, at Alexandria in Egypt, the latitude whereof he makes 30°
58′, obferved the meridian altitude of the moon when in her greateſt north
latitude at the fame time that her longitude was in the beginning of, and
found her diſtance from the zenith 2° and of a degree: fo near the zenith,
he thought parallax to be infenfible, the pole of the ecliptic being in the plane
of the meridian at the time of the obſervation, the exceſs of the moon's alti-
tude above the altitude of the higheſt point of the ecliptic, or of the tropic
of, gave the moon's greatest latitude 5°. By another obfervation of the me-
ridian altitude of the moon, near her greateſt north latitude, and in' 3° of
of b, when her true diftance from the zenith was 49° 48′, her apparent di-
ſtance was found 50°55′; the difference between theſe two diſtances is 1° 7,
which is the moon's parallax when her apparent diſtance from the zenith is
50° 55': no allowance is here made for refraction, the effects of it being un-
known in the time of Ptolemy. In the firft obfervation fo near the zenith re-
fraction is infenfible; in the ſecond, when the apparent altitude of the moon
was but 39° 5, refraction increaſed it about i, as by the table p. 255, fo
that by Ptolemy's obſervation corrected by allowing for refraction, the moon's
parallax at the altitude of 39° comes out 1°6: now by § 825, coroll. 2, as
the fine of 50° 55′ the moon's diſtance from the zenith at the time of the ſe-
cond obfervation to 1°6′ her parallax at that altitude, fo is the whole fine to
her horizontal parallax: which by calculation comes out 1°25′. This is ma-
nifeſtly too great by ſeveral minutes, and is mentioned here only to ſhew the
method: if the numbers in the prefent copies of Ptolemy be not faulty, his
obfervations were not very exact.
978 Another method of finding the parallax of the moon mentioned by
Keil lect. 21, is this: in an eclipſe of the moon, let two obfervers take the
altitudes
372
BOOK 3.
ASTRONOMY
*
altitudes of the tips of both horns, at the moment when they are both in the
fame vertical: add half the difference of theſe two altitudes to the leaſt of
them, or fubtract it from the greateſt, and you have nearly the apparent al-
titude of the center of the moon: but her true altitude is nearly equal to the
altitude of the center of the earth's fhadow at that time; now we may know
the altitude of the center of this fhadow, becauſe it is always oppofite to the
fun's place in the ecliptic, and the fun's place in the ecliptic and his depref-
fion below the horizon, and confequently the altitude of the oppofite point
of the ecliptic at any time may be known: the difference between the appa-
rent and the true height of the moon thus found is her parallax.
The horizontal parallax of the moon being known, her parallax at any
given altitude may
be thus found: as the whole fine is to the horizontal pa-
rallax, fo is the cofine of the moon's given altitude to her parallax at that al-
titude: this propofition is the converſe of that at the end of § 978.
980 The moon's distance from us being variable, by reafon of her going
round in an ellipfis in one of the focuſes of which the earth is placed, aftronomers
give us tables of the parallax of the moon, and of her diſtance from the center of
the earth, for every part of her ellipfis: the tables begin by telling what the
moon's horizontal parallax and diſtance is when in the point of her apogee;
where the diſtance is greateſt, and the horizontal parallax leaft; and proceed
to ſet down what they are for every five degrees of her anomaly, or of her
diſtance from her apogee: in the apogee the moon's anomaly is fet down o°, at
five degrees diſtance from her apogee the moon's anomaly is ſaid to be 5° at
ten degrees diſtance from her apogee her anomaly is 10°, &c. Befides that now
mentioned, there is alſo another variation in the distance of the moon from the
earth, and in her horizontal parallax, arifing from the fituation of the earth
and the moon in reſpect of the fun: for, in the fame point of her elliptic or-
bit, the diſtance of the moon from the earth will be greateſt in the quadra-
tures, and leaſt in the fyzygies: mean in the middle between the quadrature
and fyzygy, when the moon is an eighth part of a circle diſtant from the fun.
According to Sir Iſaac Newton, the horizontal parallax of the moon at her
mean diſtance from the earth, when ſhe is in fyzygy, is 57′ 30″; and her appa-
rent diameter 31′ 30″: when ſhe is in quadrature, at her mean diſtance from
the earth, her horizontal parallax is 56′ 40″; her apparent diameter 31′ 3″:
when the moon is diſtant from the fun an 8th part of a circle, and at her mean
diſtance from the earth, her diſtance from the earth is a little above 60 femi-
diameters of the earth. Gregor. aftron. 1. 4. prop. 29. The fame learned au-
thor in his principia mathem. I. 3. prop. 37, determines the mean distance of
the moon to be 60 femidiameters of the earth: this diſtance according to the
meaſure
раде 373.
V
H.
T
1
E
d
18
d
21
N
a
Book III.
16
E
E
d
17
19 M
N
a
M
22.
FE
N
a
1
}
FE
F E
d
73
20
м
a
N
23
ḍ
M
N
F
F
W. Stephens Sculp
VIND
CHAP. 3.
373
ASTRONOMY
meaſure of the earth in § 457, amounts to 240034 engliſh miles; and is fome- FIG.
thing more than it was fet down in round numbers, § 147.
981 The diſtance of the moon from the earth and her
apparent diameter
being given, the true diameter of the moon may be found by § 148. From the
apparent diameters of the moon at her mean diſtance from the earth in fy-
zygy and quadrature, fet down in the preceding ſection, her mean apparent
diameter, when at her mean diſtance from the earth and in the middle be
tween fyzygy and quadrature, is 31′ 16": from this apparent diameter and
her diſtance juſt now given of 240034 miles the moon's true diameter comes
out 2184 engliſh miles, a little more than I gave it in round numbers § 148.
From hence, the fuperficial content of the moon is equal to about a 13th
part of the ſurface of the earth, § 204.
And, the folid content of the moon is equal to about a 48th part of the folid
content of the earth, $ 205.
982 Every planet, primary or fecondary, illuminated by the fun, cafts a
fhadow towards that point of the heaven which is oppofite to the fun. If
the fun were equal to the planet illuminated by him, the fhadow would be
cylindrical, or all of the fame bignefs: as fig. 9, if the planet illuminated 9
were larger than the fun, the fhadow would grow larger as it went farther
from the planet, as in fig. 10; this ſhape of the fhadow is called calathoeides, ro
from calathos a baſket, becauſe it is fimilar to the ſhape of a baſket which
grows wider from the bottom to the top: in both theſe cafes the fhadow
would be infinitely extended from the planet. The fun being larger than any
of the planets, the fhadow of every planet enlightened by the fun is a cone
the baſe whereof is a great circle defcribed upon the planet dividing the en-
lightened from the dark hemifphere: thus the fhadow of the earth grows
leſs and lefs as it goes farther from the earth, till it ends in a point which is the
vertex of the cone, fig. 11.
983 From the magnitude of the fun and earth, their diſtance from each
other, the refraction of the atmoſphere, and the diſtance of the moon from
the earth, it is found by calculation that the ſhadow of the earth ends in a
point at a diſtance from the earth which is less than the femidiameter of the
moon's orbit; the moon therefore is not eclipfed by the shadow of the earth
alone. The atmoſphere of the earth, by refracting ſome of the rays of
the fun and reflecting others, cafts a fhadow, though not a perfectly dark
one, as an opake body does: when we fay the moon is eclipfed by paffing
into the ſhadow of the earth, the fhadow of the atmoſphere furrounding the
earth is to be underſtood: the cone of this fhadow is larger than the cone of
the earth's ſhadow alone, the femidiameter of its bafe is greater, and its axis
3 B
is
I I
374
воок 3.
ASTRONOMY
FIG. is longer; as is eaſily ſeen by fig. 12, where s repreſents the fun, abc the ſha-
12 dow of the earth, ABC the fhadow of the atmoſphere: in this figure refraction
is not confidered. The height of the atmoſphere 4A of fufficient denfity to
caſt a ſhadow is ſuppoſed to be 40 or 50 geographical miles, fee book 2,
chap. 13.
the atmoſphere reaches higher than this, but the upper part of it is
ſo thin as not to obftruct the light of the fun fo as to cauſe any fenfible fha-
dow, and is not therefore to be confidered in eclipfes. See the remarks.
984 The axis of the earth's conical fhadow, extended from the earth,
falls always upon that point of the ecliptic that is oppofite to the fun's geo-
centric place: thus if the fun's place be in the point r, the axis of the earth's
ſhadow extended from the baſe through the vertex terminates in the point ≈.
985
The height of the conical shadow of any planet, which is called alſo the
axis of the fhadow, and is the length of the cone, is greater or lefs according as
the planet is at a greater or leſs diſtance from the fun: thus the cone of the
earth's fhadow is longeſt when the earth is in aphelion, ſhorteſt when in
13 perihelion. In fig. 13 let s be the fun, when the earth is in aphelion at a,
her ſhadowy cone is EDF, the height of the fhadow is AD; when the earth
is in perihelion at P, her ſhadow is HCI, the axis of the ſhadow is P C, which
is leſs than AD: for EDF is the angle under which the fun's apparent dia-
meter is ſeen from D, at the diſtance SD; and HCI is the angle under which
the fame diameter is feen from c, at a leſs diſtance sc: therefore the angle
EDF is less than HCI, § 242: and the cones HCI and EDF having equal
baſes, the cone EDF will be longer than the cone HCI, becauſe more acute,
$ 185.
986 The earth's conical fhadow always ends in a point at a leſs diſtance
from the earth than the diftance of the orbit of mars from the earth's orbit;
and therefore mars can never fall into the ſhadow of the earth: much leſs
can jupiter or faturn, whofe orbits are at much greater diftances from the or-
bit of the earth, than the orbit of mars.
From § 917 and 669, the perihelion diſtance of mars from the fun comes
out 28480 femidiameters of the earth, from which ſubtracting the mean di-
ſtance of the earth from the fun, 20600 femidiameters, § 917, we ſhall have
nearly the leaſt diſtance that mars can ever be from the earth, 7880 femidia-
meters of the earth; but the greateſt height of the ſhadow of the atmoſphere
is not more than 220 femidiameters of the earth, and confequently that ſha-
dow can never reach mars.
987 The height of the cone of the ſhadow of the atmoſphere is always
greater than the diſtance of the moon from the earth; and therefore, if the
moon

page 375.
Book III.
1. Pal. Maroctis
2. M. Audus
3. M. Porphyrites
4. Loca Paludosa
5. Cataractes M.
6.M. Troicus
7. Atlas minor
8. Atlas major
9.J. Malta
10.M.Neptunus
11. Etna M.
12. J. Creta
110
100
1.J.Vulcania
14. J. Corsica
15. L. Niger major
16. Argentarius M.
17. Mare Adriaticum
18. Mn. Mortuum
19.
Sinai M.
20. M. Carpathes
21. M. Serrorum
22. J. Besbicus
23. Byzantium
24. M. Didymus
100
24
60
0
60
50
001
070
000
50
40
30
30
90
20
10
360
330
C
G
016
25
P26
066
360
24
34
12
OF
ICH
36
280
25. M. Libanus
26. J. Macra
27. Apollonia
28. M. Moschus
29. Thospitis L.
30. M. Herculis
31. Amadoci Montes
32. M. Riphai
33. Corax M.
34.J. Major
35. Petra Jogdiana
36. Nerofus M.
20
A Mare Boum
B S.Sirbonis
C Mare Mediterran:
D Mare Pamphilium
E Mare Hyperboreum
F Propontis
Ġ Pontus Euxinus
H J. Extremus Ponti
I S. Cercinites
KL.Corocondamehis
1. Palus Maotis
M Mare Caspium
СНАР. 3
ASTRONOMY
375
moon in oppofition be in or near one of her nodes, fhe will fall into that FIG.
ſhadow and be eclipfed.
72
The height of the fhadow of the atmoſphere is never lefs than 212 femi-
diameters of the earth, the greateſt diſtance of the moon is not more than
femidiameters: confequently the moon in or near to a central oppofition
muſt fall into the ſhadow of the atmoſphere.
988 At the fame diſtance of the earth from the fun, the nearer the moon
is to the earth the larger is the fhadow where ſhe paffes through it, becauſe
nearer to the baſe of the cone: thus, fig. 14, if the moon be in apogee, the 14
arc AF is part of her orbit, and ſhe paffes through the fhadow where its
diameter is BC; if the moon be in perigee, the arc PG is part of her orbit,
and the paffes through the ſhadow where its diameter is D H, greater than B C.
989 The conical fhadow of every planet is encompaffed with a penumbra
or thinner ſhadow; the penumbra is all that ſpace furrounding the fhadow
into which the rays of light can come only from fome part of that half of
the globe of the fun which is turned towards the planet, all the reſt being
intercepted by the planet: the penumbra is in ſhape a piece of a cone, the
vertex of which cone is between the fun and the planet: as the penumbra goes
farther from the planet, it increaſes in largenefs, being of the ſhape called
calathoeides, and therefore its extenfion in length is indefinite, § 982; the axis
of it coincides with the axis of the fhadow: in fig. 15, let s be the fun, E a 15
planet, the penumbral cone is F H G, the axis of it is H C, the vertex H, which
is the point where any two lines, as IG and LF, drawn tangents to the ſun
and the planet on oppofite fides, interfect one another.
We may imagine the penumbral cone to be generated in this manner, the
point н remaining immoveable, let IG or Lindefinitely extended be turn- 15
ed round, always paffing through the point н and touching the fun and the
planet E, and there will be generated an indefinite conical ſurface F H G, Com-
prehending befides the cone AH B, both the ſhadow A CB, and the circum-
ambient ſpace FAC, CBG, which ſpace is the penumbra.
}
990 The nearer any part of the penumbra is to the ſhadow, the lefs light
does it receive from the fun; the farther off any part of the penumbra is from
the ſhadow, the more is it enlightened by the fun: thus fig. 15, the parts of 15
the penumbra near M are illuminated by thofe rays of light only which come
from a ſmall part of the fun's globe near to 1, all the reft being intercepted
by the planet E: in like manner, the parts about N can receive only the light
that comes from a ſmall part of the fun near to L, whereas the parts of the
penumbra at p and q are enlightened in a much greater degree: for the pla-
net intercepts from P only thofe rays which come from a fmall portion of
3 B 2
the
376
BOOK 3.
ASTRONOMY
FIG. the fun near L; and hides from Qonly a ſmall part of the fun near 1. As for
thoſe parts of ſpace which are out of the penumbra, as T and v, they are en-
tirely illuminated by the fun, none of his rays being intercepted from them
by the planet E.
15
991 In order to know what part of the fun's light is intercepted from any
16 point within the penumbra, as o, fig. 16, imagin a line to be drawn from
o extended beyond the fun, as OT, and to be carried round always touching
the planet E, this line would deſcribe the conical ſurface Tov, which cuts
off from the fun's globe the fegment abcd, this ſegment could not be ſeen
at O, the rays of light coming from it towards o being intercepted by the
planet E; and therefore the diſk of the fun feen from o would appear as in
17 fig. 17, only the bright part aecb being visible.
992 The moon paffes through the penumbra before fhe enters into the ſha-
dow of the atmoſphere: this cauſes her gradually to looſe her light, which is not
fenfible at first, but, as he goes into the darker parts of the penumbra, the
grows paler, juft before her entrance into the fhadow: in effect, the penum-
bra where it is contiguous to the ſhadow is ſo dark, that it is difficult to diſ-
tinguiſh it from the ſhadow; eſpecially at the beginning or end of a lunar
eclipſe. When the moon is entered a little way into the fhadow, the edge of
the ſhadow feen upon the moon's diſk is better defined; ſo that it is eaſier to
determin the time when the edge of any ſpot in the moon firſt touches the
fhadow, than it is to determin the moment when the edge of the moon's diſk
firſt touches it, and begins the eclipfe: it is alſo eaſier to determine the time
when a ſpot leaves the ſhadow, than the time when the diſk of the moon
gets clear of it, and ends the eclipſe.
993 We
may imagin the cone of the earth's fhadow to be cut through at
the diſtance of the moon's center from the earth by a plane indefinitely ex-
tended every way parallel to the bafe of the cone: this fection will be a cir-
cle, which I ſhall call the circle of the earth's ſhadow: the center of this cir-
cle is always in the plane of the ecliptic. The circle of the earth's fhadow
when the earth is at the fame diſtance from the fun, is greater, the nearer
the moon is to the earth § 988. The circle of the earth's fhadow is greater, when
13 the moon is at the fame diſtance from the earth, the farther the earth is from
the fun §985. The apparent femidiameter of the moon in her fyzygies is about
15: the femidiameter of the circle of the earth's fhadow, is nearly three
times as great as the femidiameter of the moon..
994 If the moon in oppofition be in the node, the eclipfe of the moon will
18 be total and central, fig. 18: if very near the node,, total, but not central,
19 fig. 19: if fo far from the node that only part of her falls into the ſhadow,
the

page 377.
1. Grimaldus
2. Galileus
3. Aristarchus
4. Keplerus
5.
Gassendus
6. Schikardus
7. Heraclides
8. Harpalus
9. Lansbergius
10. Reinholdus
11. Copernicus
12. Bulialdus
1
13. Eratosthenes
14. Timocharis
15. Plate
16. Archimedes
17. Sinus Estuum
18. Pitatus
19. Tycho
20. Eudoxus
21. Aristoteles
22. Manilius
23. Menelaus
24.
Albategnius
25
HO
อย
B
18
15 O
BOOK HI
Book III.
25. Regiomontanus
26. Posidonius
27. Plinius
28. Catharina Cyrill, Theophil.
29. Fracastorius
28
H
30
HO
31
35
32
30. Censorinus
31. Meshala
32. Cleomedes
33. Proclus
34. Langrenus
35. Petavius
36.Snellius & Furnerius
A.Oceanus Procellarum
B. Mare Humorum
C. Mare Imbrium
D. Mare Nubium
E..Mare Frigoris
F. Mare Vaporum
G. Mare Serenitatis
H.Mare Nectaris
1. Lacus Somniorum
K. Palus Somni
L. Mare Crisium.
M.Mare Fecunditatis
СНАР. 3.
377
ASTRONOMY
the eclipſe is partial, fig. 20: if ſo far from the node, that the diſtance of her FIG,
center from the center of the circle of the earth's fhadow is greater than the 20
fum of the femidiameters of the fhadow and of the moon, as fig. 21, or e- 21
qual to that fum, as fig. 22, fhe will not be eclipfed at all.
995 The moon is ſometimes in the middle of a total eclipſe inviſible, in
fome places and not in others, becauſe of the different conftitution of the air,
v. Hevelii felenograph. p. 117. but generally the appears of a dufky reddiſh
colour, eſpecially towards the edges, being more dark about the middle of
the ſhadow: this colour is owing to the rays of the fun, or to the light of the
fun's atmoſphere refracted through the earth's atmoſphere, or to the light of
the ſtars and planets; moſt probably to the first of thefe: the red-making
rays being leaſt ſubject to refraction or reflection, may paſs through the at-
moſphere in the greateſt quantity, § 765. v. Kepl. epit. aftronom. p. 870. Ric-
ciol. l. 5. p. 306. Greg. aftron. lib. 1. prop. 18. Mem. d'Acad. ann. 1704.
22
996 The fun or moon feen from the earth, or the earth feen from the fun
or moon, though ſpherical, by reaſon of their diſtance, appear like circular
`planes: theſe circular planes are called the diſks of the fun, earth or moon. The
apparent diameter of the diſk of the fun or moon is by aftronomers divided
into 12 equal parts, which are called digits: each digit into 60 parts, which
are called ſcruples or minutes: as many of theſe digits and fcruples as are co-
vered by the ſhadow in the middle of a partial lunar eclipfe, fo many digits
and ſcruples of the moon are faid to be eclipfed. In a total eclipfe of the
moon without ſtay, the moon is eclipfed 12 digits, fig. 23: in a total eclipſe 23
with ſtay, ſhe is faid to be eclipſed ſo many digits as are contained between
the edge of the moon neareſt to the center of the fhadow and the edge of the
ſhadow neareſt to the moon: thus, fig. 19 repreſents the moon eclipſed 15 19
digits. Greg. aftron. l. 4. prop. 39.
997 The motion of the moon in her orbit being eastward, the beginning
of a lunar eclipſe is when the caſtern edge of the moon's difk touches the
weſtern edge of the circle of the fhadow: the end of a lunar eclipſe when the
weſtern edge of the moon's diſk leaves the eaſtern edge of the circle of the
hadow: in a total eclipfe, the time the whole difk is in the fhadow is called
the fray, duration, or time of total immerfion, fig. 18, 19..
18
998 The beginning or end of a lunar eclipfe, being inftantaneous, will 19.
ſerve to diſcover the longitude, but not accurately; for, by reafon of the pe-
numbra, the beginning appears too foon, the end too late to the naked eye,
and even to the teleſcope, and not at the fame time to all eyes: for this rea-
ſon the longitudes of places determined by eclipfes, eſpecially thoſe obſerved
before the invention of teleſcopes, cannot be depended upon. Hevel. Selenogr.
6... 56.
378
воок 3.
ASTRONOMY
FIG. c. 56. The moderns, that they may have a greater number of opportunities
of determining the longitudes than the beginnings and endings of eclipſes
would afford, do it by obſerving the times of the moſt remarkable ſpots of
the moon entering into the fhadow, or the times of their emerging out of itª:
for this purpoſe, aſtronomers have given names to a great many of the moſt
remarkable fpots upon the furface of the moon, as well the bright ones as
thofe that are dark: Hevelius has denominated them from mountains, iſlands,
countries, and feas upon our earth, where he could fancy he faw any fimili-
tude between them; and, for want of that, has given a few of them fictitious
geographical names. Ricciolus has given to many of the ſpots of the moon the
names of feveral ancient and modern aftronomers, mathematicians, and phi-
24 lofophers; others he has named after the manner of Hevelius: fig. 24 is a map
25 of the moon exactly copied from Hevelius: and fig. 25 a map of the fame
from Ricciolus. Sometimes aftronomers, in obferving lunar eclipfes, firft
meaſure the moon's apparent diameter with the micrometer, and by the help
of the fame inftrument, fet down at feveral times the diſtance in minutes and
ſeconds between the points of the horns of the moon: and fometimes they fet
down at ſeveral times how many minutes and feconds of the moon's apparent
diameter are clear of the fhadow: by either of theſe methods, they get a num-
ber of inſtantaneous obfervations, in order to determin the longitudes of pla-
ces; or to find the exact time of the middle of the eclipſe, a thing of great
uſe in perfecting the theory of the moon's motion, and correcting the tables
thereofb.
999 The quantity of a lunar eclipfe depends 1st, upon the largeneſs of the
circle of the earth's fhadow, whoſe diameter may be different by § 988, 993:
2dly, upon the apparent diameter of the moon, which may be different by §
980, 3dly, cæteris paribus, upon the diſtance of the moon from her node, at
the moment of her being at the full.
1000 The duration of a lunar eclipfe depends partly upon its quantity, part-
ly upon the velocity of the moon's motion croſs the fhadow, which is the
fame as her motion from the fun. The moon's motion from the fun is ſwift-
eft when fhe is in perigee, and the duration of a central eclipſe will then be
ſhorteſt, though the moon's diameter and the diameter of the circle of the
earth's fhadow be then greateſt; becauſe the greater length of the moon's way
through the ſhadow is more than compenfated by the greater velocity of the
moon's motion. Kepl. Aſtr. p. 868. The longeft duration of a central lunar
eclipſe, that is, when the earth is in aphelion, and the moon in apogee, is ac-
a Memoires d'Acad. Phil. Tranfact: Hevel. Selenogr. p. 486. &c.
b See Flamfteed's obfervations of eclipſes in the Phil. tranſact, abr. vol. 1. pag. 314. &c.
cording
CHAP. 3.
379
ASTRONOMY
cording to Ricciolus, 3h 57 6″. The ſhorteſt duration of a central lunar eclipſe, FIG.
that is, when the earth is in perihelion, and the moon in perigee, is according
to Kepler, 3h 37′ 26", Epit. Aftron. p. 868.
1001 The limit of a lunar eclipfe is a certain number of degrees minutes
and ſeconds which if the full moon's diſtance from her neareſt node exceeds,
ſhe will not be eclipſed; if it does not exceed, ſhe will be eclipfed. Ricciol.
Almag. l. 5. p. 309. Greg. Aftron. 1.4.pr.35.Thefe ecliptic limits are variable;
greateſt, when the diameter of the circle of the earth's ſhadow and the appa-
rent diameter of the moon are both largeſt: leaſt, when thoſe diameters are
both leaſt: mean, when the fum of thofe diameters is mean. According to
Ricciolus the greateft ecliptic limit of the moon is 12° 50 from her neareſt
node, when her latitude is 1ºo 6": her leaſt limit 10°, when her latitude is
52′ 6″. Almag. l. 5. p. 310. The mean limit is ſaid by Whifton. Eclip. Calcul.
p. 5. to be about 11° 40. In any full moon that happens when the moon is
between her greateſt and leaſt limit, ſhe may or may not be eclipſed, accord-
ing as the diameters of the ſhadow and the moon are greater or leſs: in eve-
ry
full moon that falls out when the moon's diftance from her node is lefs
than the leaſt limit, ſhe muſt be eclipſed. See the remarks.
1002 To know whether there will be an eclipſe of the moon at any given
full moon; and if there will, whether partial or total, with, or without ſtay.
The time of the full moon being given, find the fun's place for that moment,
which will give the place of the center of the earth's fhadow, that is, in the
oppofite point of the ecliptic: for the fame moment find the moon's place, and
the place of that node of the moon which is then neareſt to the ſhadow, and
the angle the moon's orbit makes with the ecliptic: in fig. 19, 20, 21, 22, 23, 19
let E F be an arc of the ecliptic, abcd an arc of the orbit of the moon in 20
which ſhe appears to move according to the order of thoſe letters, MN an arc 21
of a great circle drawn through the center of the ſhadow, perpendicular to 22
the moon's path, theſe arcs being ſmall may be repreſented by ſtrait lines with- 23
out any
fenfible error. The moon is neareſt the center of the fhadow, when
her center is in the line MN. and therefore, if eclipfed at all, is then in the
middle of her eclipfe. If the diſtance of the moon's center from the cen-
ter of the ſhadow be greater than the ſum of the femidiameter of the ſhadow
and the femidiameter of the moon, as in fig. 21, or exactly equal to it, as 21
in fig. 22, there will be no eclipse: if the moon's diſtance be leſs than that fum, 22
but greater than the difference between the two femidiameters, as in fig. 20, 20
there will be a partial eclipfe, of as many digits of the moon as are then im-
merſed in the ſhadow: if the moon's diſtance be exactly equal to the difference
between the femidiameters of the moon and the fhadow, as in fig. 23, the
ecliple
23
380
BOOK 3.
ASTRONOMY
19
FIG. eclipſe will be total without ſtay: if her diſtance be leſs than the difference be-
18 tween the femidiameters, as in fig. 18, 19, the eclipſe will be total with ſtay:
that is her whole diſk will continue fome time in the ſhadow, which ſtay
will be longer or fhorter according to the length of the moon's way through
the ſhadow, and the velocity of her motion from the fun. Greg. Aftr. l. 4. p. 35.
1003 In a central eclipſe of the moon, the refraction of the earth's atmo-
ſphere will make both the luminaries appear above the horizon, in thoſe pla-
26
ces where they are really both in the horizon: thus, fig. 26, let mм be the
center of the earth, the line AB is the rational horizon to a perſon who is at
н, as it is alſo to his antipodes on the oppofite point of the earth at L, let a
be the true place of the fun, в the true place of the moon, by refraction a
ſpectator at н will ſee the fun at D, the moon at c; in like manner, his anti-
podes at L will fee the fun at E, the moon at F. The refraction of the hea-
venly bodies when in the horizon is about 33', as by the table p. 254, the
apparent diameter of the fun is not quite fo much when greateſt, pag. 333;
ſo that refraction will make the fun appear above the horizon when he is in
reality entirely below it, the fame may be faid of the moon, whofe apparent
diameter differs very little from that of the fun. Ricciol. Almag. l. 5. p. 307.
Remarks upon § 983.
1004 Kepler was the first who, by confidering refraction, made this dif-
covery, that the light of the fun in paffing through the atmoſphere of the
earth is refracted in fuch a manner that thofe rays which come from oppofite
edges of the fun's diſk muſt interfect each other, and confequently determin
the place of the vertex of the true ſhadow of the earth,at a diſtance from the
center of the earth which is lefs than the femidiameter of the orbit of the
moon; his ſcheme may be ſeen in his aftronomia optica p. 268, and in Ricci-
olus, who gives it firſt as it is in Kepler, and afterwards with fome correcti-
ons of his own, almag. l. 5. pr. 4: both theſe authors have drawn their figures
as if the atmoſphere were throughout of the fame denfity, and as if the up-
per region of the air refracted light in the fame degree as thofe parts of it
which are near to the earth, a farther correction is therefore neceffary: v.
Tacquet aftron. l. 4. c. 4. but the following lemma is firit to be premiſed.
1005 All right lines which can be imagined to be drawn from the ſame
point of the fun to any part of the earth or atmoſphere may be looked upon
as phyfically parallel; becauſe the diameter of the earth or atmoſphere com-
pared with the diſtance of the ſun from the earth becomes infenfible: the fe-
midiameter of the earth feen from the fun would be but ten feconds, equal
to
page 379
Book III.
D
H
26
A
M
E
222
A
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27
T
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XXX
28
S
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B
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OF
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76
W. Stephens Colavit
CHAP. 3.
381
ASTRONOMY
to the horizontal parallax of the fun § 824, if we fuppofe the height of the FIG,
atmoſphere to be 50 miles, the femidiameter of the earth and atmoſphere feen
from the fun would not exceed 10". In effect, the diſtance of the fun from
the earth is fo great, that not only the earth but even the orbit of the moon
ſeen from the fun would appear but as a point, and all lines drawn from the
fame point of the fun to the earth or moon are phyfically parallel, that is, do
not deviate fenfibly from paralleliſm, eſpecially at the time of eclipfes, when
the earth and moon feen from the fun would appear very near to each other.
1006 In fig. 27, let the circle KL TV repreſent the earth, GROPSH a great 27
circle upon the convex ſurface of the atmoſphere where it is denſe enough to
cauſe a ſenſible refraction: let the rays z G K and X H L tangents to the fun in
z and x, and tangents to the earth in K and L, be continued till they meet
in c: if we imagine theſe lines to revolve round the line ABC drawn through
the centers of the fun and of the earth, they would defcribe the cone K CL,
which is the fhadow the earth would caft if there were no refraction from
the atmoſphere that ſurrounds it. Now fince the line z G at its entrance into
the atmoſphere at G is refracted towards the perpendicular GB, it will not
go ſtrait on to c, but will fall upon the earth ſomewhere at v, and, for the
fame reaſon, the line x H will fall upon the earth at T; the cone KCL is not
the earth's true fhadow, as the ancients who did not confider refraction ima-
gined, but may be called the fuppofed fhadow of the earth: the axis of this cone
is B C.
1007 The Shadow of the atmosphere is the cone RDS terminated by the lines 27
ZRD and XSD tangents to the fun and to the atmoſphere, where denſe e-
nough to intercept fo many of the fun's rays as to caft a fhadow: the axis of
this cone is B D.
may
1008 As for thoſe rays which terminate the true ſhadow of the earth, they 27
muſt be ſuch as, being tangents to the fun in z and x, fall upon the furface
of the atmoſphere nearer to the points of contact R and s than the points G
and н are; fuch is the ray z M, which enters the atmoſphere at M, and, after
its firſt refraction at м, goes on ſo near the earth that, phyſically ſpeaking, it
be confidered as a tangent to the earth in к, from whence it goes on to
the point o, where coming out of the atmoſphere it is refracted from the per-
pendicular fo as to proceed to E, and is there met by a like refracted line
XNLPE. Thus the true fhadow of the earth is KOEPL, terminated by the
refracted rays z MKOE and XNLPE tangents to the fun and the earth: the
height of the true fhadow is B E.
1009 To find the angle of the cone of the fuppofed fhadow of the earth: in fig. 28
28, let s be the center of the fun, E the center of the earth, ACX, BCX, rays
3 C
tangents
382
BOOK 3.
ASTRONOMY
FIG. tangents of the fun and earth without refraction, the cone of the ſuppoſed
28 fhadow is CXD, whereof the angle at x is required: from the centers s and
E to the points of contact a and c draw the ſtrait lines SA, E C, and draw
EF parallel to AC; fince the angles at a and c are right ones, § 28, ACEF
will be a right-angled parallelogram, and confequently CE is equal to AF,
§ 57: from s A the fun's femidiameter known by § 918 take AF equal to CE
the femidiameter of the earth, known by § 457, the remainder SF will then
be found: SE is the diſtance of the fun from the earth, known by § 917, we
have then a triangle EFS right-angled at F, whereof two fides SF and SE are
given; make s E radius, and SF will be the fine of the angle FES, which an-
gle may then be found by § 140: but, AX and FE being parallel by the con-
ſtruction, FES is equal to cxE, § 47: and CXE being given, the double of
it CXD is eafily found.
28
Example. Sa is 96 femidiameters of the earthª: take from it AF equal to
CE one femidiameter, the remainder s F is equal to 95 femidiameters of the
earth. SE is 20600 femidiameters of the earth by § 917: fay then as 20600
is to 95, fo is SE 10000000 as radius to a fourth number 46116, as fine of
the angle s E F: which angle by the table of fines is 15′ 51″; the double where-
of is 31' 42".
Or thus, the femiangle of the fuppofed fhadow is equal to the apparent
femidiameter of the fun bating the fun's horizontal parallax: the fun's appa-
rent femidiameter at his mean diſtance is 16′ 2″, § 903, fubtract the fun's ho-
rizontal parallax 10", the femiangle of the fuppofed fhadow is 15 52", the
whole angle is 31′ 44″, but 2" different from that before found.
1010 To find the axis of the cone of the fuppofed ſhadow of the earth: in the
28 figure before us we have a triangle ECX, whereof the angle at c is a right
one, § 28, the acute angle at x is found by the preceding fection, the fide CE
is the femidiameter of the earth: the length of the fide Ex the axis of the
cone CXD may therefore be found in femidiameters of the earth.
I
Example. In the triangle E cx make the hypotenuſe E X radius and CE Will
be fine of the angle cx E of 15′ 51″, by § 140 cafe 1; ſay then as 46106 fine of
15′ 51″ to 1 femidiameter, fo is 10000000 radius to 217 femidiameters of the
earth, the height of the ſuppoſed ſhadow.
1011 To find the angle and axis of the cone of the shadow of the atmosphere:
28 in fig. 28 let CD now reprefent the convex furface of the atmoſphere, where
a In § 918 I fet down the fun's diameter 100 of the earth's, as being the neareſt round number to the
true one: the number 96 here made ufe of is deduced from the fun's horizontal parallax 10", § 820, and
his mean apparent diameter 32′ 5″§ 903: for the earth's femidiameter would at the diſtance of the fun
appear under an angle of 10", § 824, the fun's femidiameter at his mean difl. nce appears under an angle
of 16' which is equal to 10" multiplied by 96.
1
denfe
CHAP. 3.
383
ASTRONOMY
denfe enough fenfibly to intercept any of the fun's light, EC the femidiame- FIG..
ter of the atmoſphere, proceed as in the two fections immediately foregoing, 28
and you may find them; the axis EX will be found 217 as before, but they
will then be femidiameters of the atmoſphere, not of the earth.
Scholium. The difference between the angle of the ſuppoſed ſhadow of the
earth and the angle of the ſhadow of the atmoſphere is infenfible; the diffe-
rence between the axes of theſe two ſhadows is fmall, but about an hundredth
part of the whole heighth: v. Tacquet aftron. 1. 4. c. 2. From hence it comes
to paſs, that the ancient aſtronomers were not much out in their calculations
of eclipfes; though they did not take the fhadow of the atmoſphere into the
account: this ſhews alſo that the height of the atmoſphere where denſe e-
nough to caſt a ſhadow is not fo great as to make it neceffary to confider it
in the affair of eclipſes.
1012 To find the angle of the true shadow of the earth: the femiangle of
the cone of the true fhadow of the earth is equal to the femiangle of the
fuppofed ſhadow increaſed with the addition of double the fun's horizontal
refraction: in fig. 27 let z GKC, XHLC be the unrefracted rays of the fun
which terminate the fuppofed fhadow, z M KOE, XNL PE the refracted
rays which comprehend the true fhadow, the angle of the true fhadow is
O E P, the angle of the ſuppoſed ſhadow is K C L. Since the ray z м pro-
ceding after refraction from м to o touches the earth in K, the refracted ray
MK extended both ways to y w is the fenfible horizon of a ſpectator at к,and
confequently if zм be extended to Q, the angle QMK or its vertical z My
will be the horizontal refraction of the fun: now the rays z KC and z MQ,
being tangents to the fun, will not be fenfibly different from parallel, and
therefore the refracted ray yw interfecting them makes the angle cK w equal
to QMK the horizontal refraction of the fun, § 47. This being demonſtra-
ted, the external angle Kwв is equal to the two internal oppofites CKw the
horizontal refraction of the fun and K cw half the angle of the ſuppoſed fha-
dow: then fince Ko, inſtead of going ftrait on to w, is refracted into the line
OE, Eow is the angle of refraction at the egrefs of the ray out of the atmo-
ſphere, equal to the refraction at the ingrefs QMK: therefore KWB or OWB
together with Eow are equal to KCB the femiangle of the ſuppoſed fhadow
with double the horizontal refraction of the fun: but owв together with E ow
are equal to the external oppofite OE B: therefore o E B the femiangle of the
true ſhadow of the earth is equal to the femiangle of the ſuppoſed ſhadow
together with double the horizontal refraction of the fun. Q.E. D. This de-
monſtration is given by Tacquet and Ricciolus, wherein there feems to be this
defect, that mo is fuppofed to be a ſtrait line, whereas it is a curve whoſe
3 C 2
curvature
27
384
воок 3.
ASTRONOMY.
FIG. curvature is greateſt near K, leaſt near м and o, § 749, and 750; and there-
27 fore it does not cut the parallels z мQ, at м, and z KC, at K, with the fame
27
inclination: but if it be remembred, that all vifion is made in a ſtrait line,
and that an object at z would to the eye at к appear in the line of the laſt di-
rection, which continued is Ky; and that in like manner an object at E would
be ſeen in the line кw, we may very well take yw for the fenfible horizon
of a perfon at K.
Example. The horizontal refraction of the fun according to Flamsteed is
33', § 756, the double of 33′ is 1° 6': to 1° 6' add 15 51" the femiangle of
the cone of the fuppofed fhadow of the earth, by § 1009, and you have 1°
21′ 51″ the femiangle of the true ſhadow.
1013 To find the height of the true ſhadow of the earth: in the triangle вKO
the angle at K is a right one, Eucl. l. 3. prop. 18, the fide BK the femidia-
meter of the earth is 3967 miles, § 457; the fide BO is 4007 miles; for oa
the height of the atmoſphere is 40 miles, § 763: from theſe data the angle
KOB is by § 140 found to be 81° 53′ 51″. Produce Eo to b, and мo to w:
the angle of refraction E ow at egrefs out of the atmoſphere is equal to the
angle at ingrefs QMO: QMO is 33' the horizontal refraction of the fun, §756:
therefore Eow or its vertical bok is 33': add this 33′ to KOB of 81° 53′ 51″,
and the angle boв will be 82° 26′ 51″, and the confequent angle E OB 97
339", § 39: OEB is 1° 21′ 51″, § 1012; therefore in the triangle EBO the
fide BO and the angles EOB, OE B are given: from theſe data BE the height
of the true ſhadow of the earth may be found, by this known propofition in
trigonometry, that in all oblique-angled triangles the fides are as the fines of
their oppofite angles: by a calculation after this manner, the length of B E
comes out about 42 femidiameters of the earth. And here we may obferve
with Taquet, aftron. l. 4. c. 2. n. 16, that different heights of the atmoſphere
will make no confiderable difference in the refult of the calculation, but that
the length of the ſhadow will come out about 42 femidiameters of the earth
what ever number of miles between 1 and 100 be affumed for the height of
the atmoſphere.
The axis of the true fhadow being no more than about 42 femidiameters
of the earth, that ſhadow can never reach the moon, whoſe leaſt diſtance from
the earth is not leſs than 50 femidiameters: the axis of the ſuppoſed ſhadow
is about 217 ſemidiameters of the earth, § 1010, the axis of the ſhadow of
the atmoſphere is about 2 femidiameters longer, the ſhorteſt of theſe two
ſhadows is more than long enough to reach the moon when in oppofition,
for the moon's diſtance from the earth never exceeds 72 femidiameters of the
earth: thus the propofition advanced by Kepler mentioned § 1004 is proved
to
page 385.
M
C
B
A
29
Book III.
L
E
G
B
C
A
31
K
D
D
30
C
32
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33
M
m
m
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X
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34
F
B-
E
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77
E
M
СНАР. 3.
385
ASTRONOMY
to be true: as is alfo what was faid § 986, that the fhadow of the earth can- FIG.
not reach ſo far as to eclipſe mars.
29
1014 To find the diameter of the circle of the earth's fhadow: the firſt me-
thod I fhall mention is that of Ptolemy, l. 5. c. 14, by a lunar eclipſe, where-
of the quantity is known by obfervation, the moon's apparent diameter, la-
titude, and diſtance from the neareſt node, at the time of the middle of the
eclipſe being alſo known: fuppofe the eclipfe to be of 6 digits, fig. 29, let
EDC be the ecliptic, A M B the circle of the earth's fhadow, the center where-
of D is in the ecliptic: in the middle of the eclipſe, if it be of 6 digits, or
half the moon's diameter, the center of the moon will be in the circumference
of the ſhadow in the point м, and then DM is the femidiameter of the fha-
dow, not fenfibly different from MG the moon's latitude: If the eclipſe be
of leſs than 6 digits, as in fig. 30, of a 4th part of the moon's diameter 30
HF, the femidiameter of the fhadow DF wants juft as much of being equal
to the moon's latitude DM, as HF the 4th part of the moon's diameter is lefs
than the moon's femidiameter HM. If the eclipfe be of more than 6 digits,
add to the latitude of the moon the number of minutes and feconds of the
moon's diameter which are eclipſed over and above her femidiameter, and
have the femidiameter of the ſhadow.
you
1015 A fecond method is thus: fig. 31, let BL C be the fun, K HD the earth, 31
CX and BX tangents to the fun and earth, K X D the fhadow of the earth, which
may be taken inſtead of the ſhadow of the atmoſphere, as not being fenfibly
different from it, §1011, Mm an arc of the moon's orbit; F E will be the cir-
cle of the earth's fhadow, QE the femidiameter of that circle, which ſeen
from the earth would appear under the angle QAE: to find this angle, pro-
ceed thus; ax being found by § 1010, take from it AQ the moon's diſtance
from the earth, and the remainder ox will be known: Here is then a tri-
angle X QE, right-angled at Q, whereof the fide ox is known, and the angle
QXE, being the femiangle of the cone, is given by § 1009, therefore the ra-
tio of ox to QE, may be found by § 147: moreover, in the triangle QAE,
fince the fides AQ and QE are known, the angle QA may be found, by § 140.
1016 From the horizontal parallax of the moon, the apparent diameter
of the fun, and the femidiameter of the fhadow, Hipparchus, and after him
Ptolemy attempted to find the fun's diſtance from the earth: but an error in one
of theſe data alone will cauſe a great error in the diſtance of the fun fo dedu-
ced; this method therefore of inveſtigating the fun's diſtance is juſtly reject-
ed by aſtronomers: a much better way of finding the fun's horizontal paral-
lax, and confequently his diſtance from the earth was ſhewn § 820.
1017 A third method of finding the femidiameter of the circle of the earth's
fhadow
386
воок 3.
ASTRONOMY
FIG. fhadow is this of Kepler, epit. aftr.p.862. from the fum of the horizontal pa-
rallaxes of the fun and moon fubtract the apparent femidiameter of the fun,
the remainder is the apparent femidiameter of the circle of earth's fhadow,
31 feen from the earth: Demonftration, fig. 31, draw the lines CAG, AE and
AD: fince AD is perpendicular to CDE, § 28, ACD is the fun's horizontal
parallax, and AED the moon's, to theſe two angles the external angle G A E
is equal, Eucl. 1. 32. from G A E take GA Q, or its equal, becauſe vertical, sac,
the fun's apparent femidiameter, the remainder is QA E the femidiameter of the
circle of the earth's fhadow: example; at the moon's mean diſtance her ho-
rizontal parallax is 57 30", § 980, add the fun's parallax 10", the fum is
57′ 40″; ſubſtract from this ſum 16′ 2″, the fun's femidiameter at his mean
diſtance, § 903, the remainder 41′ 38″ is the femidiameter of the circle of
the earth's fhadow.
32
Remarks upon § 1001.
1018 The mean apparent diameter of the moon has been given, § 980;
her greateſt and leaft apparent diameters muſt alfo be known, before the e-
cliptic limits can be determined. The apparent diameter of the moon may be
found, by the ſame methods as were taught of finding that of the fun § 902,
904, 907. Mouton made a great number of obfervations of the fun's appa-
rent diameter, and ſome of that of the moon; he meaſured them by the time
of the tranfits of the diſks of thoſe luminaries croſs the plane of the meridi-
an, or of ſome other hour circle, with a pendulum which made 9550 fwings
in an hour: we have a full account of thoſe, and fome other aftronomical
obfervations, in his obfervationes diametrorum folis et lunæ apparentium &c.
Lugduni 1670. The greateſt apparent diameter of the fun obferved by Mou-
ton was 32′ 32″: the leaſt 31′ 29″: near enough to fome of the beſt we have,
§ 903. The greateſt apparent diameter of the full moon obferved by him in
perigee was 33′ 29″: he gives us no obfervations of the moon's leaft diameter
when near her apogee: his method was that mentioned § 902, only he took
tranfits croſs other hour circles as well as croſs the meridian; by which means
he was able to take a great many tranfits in a day. In taking tranfits of the
moon for this purpoſe, her apparent horary motion in right aſcenſion at the
time of the obfervation muſt be known; that fo much of it as anſwers to the
time of the tranfit of the whole diſk of the moon may be ſubtracted from the
number of feconds of time by which her apparent diameter is meaſured.
1019 In fig. 32, let ABCD be the circle of the earth's fhadow, AE the e-
cliptic, EG the moon's path, GF part of a circle of latitude drawn through
G the center of the moon, and r the center of the ſhadow, at the moment
of
CHAP. 3.
387
ASTRONOMY
of fyzygy, and all theſe projected upon the ſphere of the moon's orbit: the FIG.
moon's latitude is then GF, which line, though not perpendicular to the 32
moon's path, and confequently not the leaſt diſtance between the centers of
the moon and of the fhadow as HF is, differs not fenfibly from it: the femi-
diameter of the ſhadow BF when largeft is 45 10", the femidiameter of the
moon GB when largeft is 16′ 40″, the fum of theſe is 61' 50", if the latitude
of the moon at the full exceeds this fum there can be no eclipfe. To find the
greatest limit of lunar eclipfes; in the figure before us EFG is a triangle right 32
angled at F, the fide GF is 61′ 50″, the angle at E is 5° 17 the inclination of
the moon's orbit to the ecliptic in fyzygy: from theſe data the fide E G will
be found 11° 16′: if the diſtance of the full moon from her neareſt node ex-
ceeds this fhe cannot be eclipfed. The leaft femidiameter of the moon is 14
45", of the ſhadow 37′ 40″, the fum of theſe is 52′ 25″, if the latitude of the
moon at the full be leſs than this fum, ſhe muſt be eclipfed. To find the leaft
limit of lunar eclipfes: in the figure before us, if the fide GF be 52′ 25″, the
fide FE will come out 9° 32, if the diſtance of the full moon from her neareſt
node be leſs than 9°32′, ſhe muſt be eclipſed.
Cor. If the diſtance of the full moon from her neareſt node be more than
9°32′, and leſs than 11° 16′, there may be a partial eclipſe of the moon, or
The may eſcape being eclipfed; according as the femidiameters of the moon
and the ſhadow are greater or lefs at the time of the ſyzygy.
1020 The argument of latitude of the moon at any time is the arc of the
moon's orbit which, proceding according to the order of the figns, reaches
from her afcending node to her place in her orbit, at that time: of ſo many
degrees minutes and feconds as that arc contains, the argument of latitude is
faid to be: the word argument ſeems here to be uſed in a logical fenfe, and
fignifies the arc by the knowledge of which the moon's latitude is founda.
1021 The moon's anomaly is either mean or trueb: the mean anomaly of the
moon is her diſtance from her apogee proceding according to the order of the
figns, computed upon a fuppofition that ſhe has been carried all the while e-
quably in her mean motion: the true anomaly of the moon is her true diſtance
from her apogee, computed by making allowance for the unequability of her
motion: as the true motion of the moon is fometimes fwifter fometimes flow-
er than her mean motion, in order to find her true anomaly, we muſt ſome-
times add to her mean motion, and fometimes fubtract from it.
a Argumentum eſt arcus per quem alium arcum quærimus: dicitur analogice ad logicam. Vitalis lexicon
Mathemat.
b See § 776. and 980.
1022
388
BOOK 3.
ASTRONOMY
FIG.
1022 Aftronomers give us tables wherein the latitude of the moon is fet
down for every degree of her argument of latitude. There are alſo tables
wherein the horizontal parallax and apparent femidiameter of the moon are
fet down for every 5th or 6th degree of her anomaly §980. The diftance of the
moon from the center of the earth being about 60 femidiameters of the earth,
the difference between the diſtance of the moon in the zenith and of the fame
in the horizon is confiderable; being about a 6oth part of her whole diſtance
or one femidiameter of the earth: this caufes a fenfible difference in the appa-
rent diameter of the moon, when ſhe is in different altitudes. The diſtance of
the fun from the earth being about 20600 femidiameters of the earth, the
difference between the fun's diſtance from us when in the zenith from what
his diſtance is when he is in the horizon is inconfiderable; being only a 20600th
of the whole diftance of the fun: and therefore his different altitude does not
33 cauſe
any fenfible difference in his apparent diameter. In fig. 33 let ABD be
the earth, Hz the orbit of the moon; fuppofing the moon's diſtance from the
center of the earth to continue the fame during the time of her motion from
the horizon to the zenith, cz and CH will be equal: if a fpectator at A has
the moon in his horizon at H, the diſtance of the moon from him is н A,
nearly equal to CH; but if the moon be in his zenith at z, her diſtance from
him is z A, leſs than CH by CA a femidiameter of the earth: the moon's ap-
parent diameter is therefore leaſt in the horizon, and increaſes gradually as
fhe riſes higher towards the zenith. There are tables wherein is fet down
what the increaſe of the moon's apparent diameter is, for every degree of al-
titude from the horizon to the zenith.
34
Remarks upon § 1002.
1023 The way of the diſk of the moon through the circle of the earth's ſhadow
would be the fame as the way of the moon in her orbit from the ecliptic, if
the ſhadow continued in the fame place during the time of an eclipfe; but by
the daily motion of the earth in her orbit, the fun and the ſhadow of the
earth both appear to go on in the ecliptic, according to the order of the figns:
this motion of the fhadow muſt be taken into the account in a lunar eclipfe,
in order to find in what manner the moon paffes through it. In fig. 34, let
& E be the ecliptic, Mm part of the moon's orbit, AB the circle of the earth's
ſhadow, if the ſhadow ſtood ſtill while the moon paffes through it in the di-
rection мm, ſhe would croſs the ſhadow in the line bl, making with AB
which may be called the ecliptical diameter of the fhadow, as being that dia-
meter of it which is coincident with the ecliptic, the angle m E, equal to
what the inclination of the moon's orbit to the ecliptic is at that time; but
becauſe
page 389.
B
Book III.
C
A
35
N
0
M
L
78
B
C
A
N
M
a
37
B
A
D
38
E
C
UNIV
OF
WS.
CHAP. 4.
389
ASTRONOM Y
becauſe the ſhadow is moving flowly on from & towards E, at the fame time FIG.
that the moon is moving fafter from 2 towards m, at the end of a fhort gi- 34
ven time, fuppofe one hour, let the moon be got to m, the fhadow to F, the
line of the moon's apparent motion through the fhadow is now Fm, which
makes the angle mFE with the ecliptic diameter of the ſhadow CD: this an-
gle is greater than m & E, Eucl. 1. 32: and for any time a little longer
or fhorter than one hour, the time fuppofed, whilſt the moon and ſhadow
continue to move in velocities having the fame ratio, the line which exhi-
bits the moon's way from the ſhadow will be parallel to Fm, and make the
fame angle with the ecliptic diameter of the fhadow. If the motion of the
moon be flower, or the motion of the fhadow quicker than in the ratio
before ſuppoſed, ſo that, for example, the moon goes only to p while the
ſhadow goes to F, the angle made by the line of the moon's motion with the
ecliptical diameter of the ſhadow will then be PF D, greater than mFD: if on
the contrary the motion of the moon be quicker, or that of the ſhadow flow-
er than was ſuppoſed, ſo that the moon goes to Q while the fhadow goes to
F, the moon's way from the fhadow will be FQ, which makes with the e-
cliptic diameter of the ſhadow the angle QFD, leſs than mFD.
1024 Aftronomers give us tables wherein are ſet down the different angles
which the way of the moon from the fun makes with the ecliptic, according
to the difference of the moon's motion from the fun, and the different di-
ſtances of the moon from her node, in order to fhew the path of the moon
through the ſhadow of the earth, in a lunar eclipfe; or the path of the moon's
fhadow upon the difk of the earth, in an eclipſe of the fun: but, as the uſe
of theſe tables is chiefly for calculating eclipfes, they extend no farther from
the moon's nodes than the ecliptic limits.
CHAP. 4. OF ECLIPSES OF THE SUN.
1025 Sometimes the moon in conjunction, being in or near one of her
nodes, is interpofed between us and the fun, and confequently hides the fun,
or part of him from us, and cafts a fhadow upon the earth: this is called an
eclipfe of the fun; and may be total, or partial. An eclipſe of any lucid bo-
dy is a deficiency or diminution of the light which would otherwife come
from it to our eye, caufed by the interpofition of fome opake body. The e-
clipfes of the fun and moon, though expreffed by the fame word, are in na-
ture very different: the fun in reality loofes nothing of his native luftre in the
greateſt eclipſe, but is all the while inceffantly fending forth ſtreams of light
3 D
Very
390
воок 3.
ASTRONOMY
}
FIG. every way round him, as copiouſly as ever; only fome of thoſe ſtreams are
intercepted in their way towards our earth, by the moon coming between
the earth and the fun: and the moon having no light of her own, and receiving
none from the fun on that half of her globe which is towards our eye, muſt
appear dark, and make ſo much of the fun's diſk appear to be dark or defi-
cient, as is hid from us by her interpofition. The moon, when ſhe is eclip-
fed, having no light of her own, fuffers a real diminution of her borrowed
light, by the earth coming between her and the fun, and ſtopping the
rays of
the fun in their paffage towards the moon. What is called an eclipſe of the
fun is in reality an eclipte of the earth, which is deprived of the fun's light,
by the moon coming between and caſting a ſhadow upon it. The earth be-
ing a globe, only that half of it which at any time is turned towards the fun is
enlightened by him at that time; it is upon fome part of this enlightened half
of the earth that the moon's fhadow or penumbra falls in a folar eclipfe.
1026 The moon being much leſs than the earth, her conical fhadow can
fall only on a ſmall part of the earth at a time: to the inhabitants of that
part
of the earth on which the ſhadow falls, the eclipfe will be total: to thoſe in
the middle of the fhadow, central: to thofe within the penumbra of the moon,
that is, without the fhadow, but ſo near it that part of the fun's diſk is hid
by the interpofition of the moon, partial: to thoſe without the penumbra,
35 there will be no eclipſe at all. Thus, fig. 35, let ABC be the fun, MN the
moon, мg/N part of the cone of the moon's fhadow, мdefNbg the penum-
bra of the moon: it is eafy to fee, 1, that thoſe parts of the earth which are
within the circle reprefented by gb are covered by the fhadow of the moon,
and that no rays can come from any part of the fun into any part of that cir-
cle, by reafon of the interpofition of the moon: 2, in thoſe parts of the earth
whereon the penumbra falls, only part of the fun is vifible: thus, any where
between d and g the parts of the fun near c cannot be feen, the rays coming
from thence towards d or g being intercepted by the moon; whereas, at the
fame time, the parts between ƒ and b are illuminated by rays coming from c,
but are deprived, by the interpofition of the moon, of fuch as come from A:
3, the nearer any part of the earth within the penumbra is to the ſhadow
of the moon, as in places near g, lor h, the leſs portion of the fun is viſible to
its inhabitants; the nearer to the outſide of the penumbra, as near d or e orf,
the greater portion of the fun may be feen: 4, out of the penumbra, as at p
or qor s, the entire difk of the fun is vifible.
Corol. In any place where the eclipfe of the fun is total, the outfide of the
penumbra firſt paffes over it, then gradually the parts of the penumbra near-
er to the ſhadow, then the fhadow, then fucceeds the penumbra, firſt the
parts
CHAP. 4.
391
ASTRONOMY
of it neareſt to the ſhadow, and then after them, gradually thofe near- FIG.
parts
er the outſide, till the whole penumbra has left the place; thus, in the figure 35
before us, by the moon's motion in her orbit in the direction L M N O, the ſha-
dow and penumbra will appear to go in the direction df, ſo that, in any place
as g or h, for example, as the penumbra firſt, and afterwards the ſhadow, and
then the penumbra again advance over it, the moon appears to the inhabi-
tants firſt to touch the edge of the fun's diſk, proceeds to cover more and
more of it, till the eclipfe becomes total; after that, the moon appears to go
gradually from off the diſk of the fun, till his whole diſk is again viſible.
1027 The quantity of a folar eclipfe in general, is the largeneſs of the moon's
ſhadow and penumbra projected upon the earth; theſe are largeſt when the earth
is in aphelion and the moon in perigeea. The quantity of a folar eclipfè in any place
is thus determined: to thoſe within the line which the center of the moon's ſhade
deſcribes upon the earth, if the apparent diameters of the fun and moon be ex-
actly equal, the eclipfe will be barely total: if the diameter of the moon be greater
than the fun's, it will be more than total: if the diameter of the moon be leſs
than the fun's, the eclipſe will be annular, that is, the fun's difk will not be
entirely covered, but there will be a ring of his light viſible round the diſk of
the moon. Eclipfes may be alfo total, or annular, in places a little diftant from
the
way of the center of the ſhade, but not central. More than total eclipfes
appear greateſt in thoſe places which are neareſt the path of the center of the
ſhadow. Partial eclipſes appear greateſt in thoſe places which are neareſt the
way of the moon's ſhadow upon the earth. The quantity of a folar eclipfe in
any place is eſtimated by the number of digits of the fun's diameter that ap-
pear covered by the diſk of the moon, to the inhabitants of that place, in the
middle of the eclipſe: in an eclipſe barely total, the fun is eclipſed 12 digits:
when the eclipfe is more than total, he is eclipfed fo much more than 12 di-
gits, as the diſtance between the edges of the difks of the fun and moon a-
mounts to, in thoſe points where thofe edges are neareſt to each other; which
is the line ab, fig. 36.
1028 The Shape of the moon's fbadow projected upon the earth in the middle
of the eclipfe depends upon the moon's diſtance from her node. If the moon
is in her node, the centers of the fun, moon, and earth, are all in a ſtrait line,
which is perpendicular to the ſpherical furface of the earth; and therefore the
projection of the moon's fhadow upon the diſk of the earth will be a circle.
When the moon has latitude, the axis of her ſhadowy cone makes an oblique
angle with the ſpherical furface of the earth; and therefore the projection of the
ſhadow upon the earth's difk will be an ellipfis, which will be more ob-
long, the greater the moon's latitude is. In the folar eclipfe A. D. 1715, the
3 D 2
longeſt
a § 1029.
36
392
воок 3•
ASTRONOMY
FIG. longeft axis of the elliptic fhadow was 170, the ſhorteſt axis 1 10 geographical
miles, or minutes. Phil. tranfact. n. 343. If a terreftrial globe be placed in
the fun, and a ſmall round ball carried along between it and the fun, the ſha-
dow of the ball at its firft entrance upon the globe will be a long oval, which will
grow fhorter as the ball is brought nearer to fuch a fituation as to have its
center in a line drawn through the centers of the fun and the globe; there the
ſhadow of the ball will be a circle: but will grow again into an ellipfis, more
oblong as the ball is carried on, till the fhadow of it has left the globe.
1029 The largeness of the moon's fhade projected upon the earth depends up-
upon theſe lemmata. The conical fhadow of the moon is longer, and fimilar
fections of it at equal diftances from the moon are larger, the greater the
moon's diſtance is from the fun, § 985. Therefore the projection of the moon's
fhadow upon the earth is largeſt, when the earth is in aphelion and the moon
in perigee; leaſt, when the earth is in perihelion, and the moon in apogee,
at the fame time, § 985. In a folar eclipſe that is central and barely total in
any place, the vertex of the moon's fhadow does but juſt reach the furface of
the earth, in that place.
In any place where the eclipse of the fun is annular, the tip of the cone of
the moon's ſhadow does not reach the furface of the earth in that place. An
eclipſe of the fun may be total near the middle of the difk of the earth, and
37 annular in places near the edges of the diſk: thus, fig. 37, let MN be an arc
of the moon's orbit, DbE the half of the globe of the earth that is turned to-
wards the fun in the middle of a ſolar eclipfe, when the moon is at A, her ſha-
dow does not reach fo far as a; in that place therefore, the eclipfe will be an-
nular: when the moon is at B, the ſhadow reaches to b; there the eclipſe is
total: when the moon is at c, the ſhadow does not reach to c; there the e-
clipſe is again annular.
The firſt annular eclipſe recorded by any aftronomer to have been obferved
was that of the year 1567, taken notice of by Clavius, who ſaw it at Rome,
and was in doubt whether the like had ever happened before or not: where-
as eclipſes central or nearly central muſt always be annular, when they fall out
at a time when the moon's apparent diameter is leſs than that of the ſun;
which was the cafe in the folar eclipſe of A. D. 1748 july the 14th, the be-
beginning of this eclipſe at Cambridge was 9h 5′ 18″ in the morning, the end
12h
9′ 41″ apparent time; the apparent diameter of the fun was then 31′ 46″,
of the moon 29′ 34″ by the tables: near the time of the middle of this eclipfe,
I let the fun ſhine into a dark room, through a teleſcope of about 8 feet, up-
38 on a white paper fixt at ſuch a diſtance from the eye-glaſs that his picture
paper was of the dimenſions of the outermoft circle ABC, fig. 38;
upon the
the
Book III.
79
39
L
N
a
P
L
e
M
C
k
g
P
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B
40
41
L
A-
D
A-
-D
E
E
A
E
L
A
H
E
43
P
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44
D A
E
D
UNIL
OF
Ow
45
P
42
D
W.S
D
P
1
r
CHAP. 4.
393
ASTRONOMY
the inner circle def reprefents the apparent magnitude of the diſk of the moon FIC.
taken at the ſame time, by marking three points in the circular edge of the
moon's ſhadow, and drawing a circle through thoſe points; Eucl. 4. 5.
1030
The way of the moon's ſhadow upon the earth is generally from weft
to eaſt; inclining towards the north, if the moon be in or near her aſcending
node; as in the total eclipfe of the fun april the 15, A. D. 1715: but inclining
towards the fouth, if the moon be in or near her defcending node; as in the e-
clipſe of may the 11, 1724: as in that alſo of july the 14, 1748. The way
of the ſhadow upon the earth may fometimes be from east to west; but this
can happen only to thoſe who live within the polar circle, and muſt fall out
when their oppoſite meridian, defcribed § 300, is turned towards the fun or
nearly fo: let fig. 39 be a projection of part of the earth's enlightened diſk; 39
in reſpect of the rectilinear meridian Pf, the meridians on the right hand in
the figure, Pg, Ph, Pi, &c are eaſtern; the meridians on the left hand pa, pb,
&c are weſtern: fo that, the center of the fhadow of the moon, paffing along
the line abcd &c according to the order of the letters, goes upon the earth
from weft to eaſt. But if the fhadow paffes on the other fide of the pole, as
in the line qrftuy, according to the order of the letters, the way of the ſha-
dow will be from east to west: for, in reſpect of the meridian PM, the meri-
dians on the right hand in the figure, Ps, Pt, Pu, are weſtern; thoſe on the
left hand as pq, Pr, Ps, are eaſtern.-The way of the center of the moon's
ſhadow is a ſtrait line, only when it defcribes a diameter upon the diſk of the
earth; otherwiſe it is an elliptic curve, but fo near to a ftrait line that it may
be repreſented by one, without fenfible error.
1031 Eclipſes of the fun may be confidered two ways; 1,as they appear to
us in the heaven; 2, as they would appear to a fpectator placed in the moon; as
to the firſt of theſe, the inhabitants of different parts of the earth, ſee the moon
in different points of the heaven, at the fame moment of time: this is owing
to the moon's parallax, by reafon whereof, a fpectator who has the moon in
his horizon at a given time, views her in the heaven at the diſtance of about
one degree, or almoſt double the ſun's apparent diameter from the place where-
in ſhe appears at that time to him who has her in his zenith, § 980; where-
as the parallax of the fun is ſo ſmall as not fenfibly to change his place, but,
at any given moment of time, he appears in the fame point of the heaven to
all the inhabitants of that half of the globe of the earth which is then illu-
minated by him: from hence it comes to paſs that, at the fame time that the
inhabitants of one part of the earth fee the fun quite covered by the moon, to
thoſe who live at a confiderable diftance from them, only a part of him ap-
pears to be hid; others who live ſtill farther off do not fee him eclipfed at all:
and,
394
BOOK 3.
ASTRONOMY
FIG. and, according as they are in different fituations, men behold the upper or
lower the eaſtern or weſtern edge of the fun, as alfo more or leſs of the
fun's diſk eclipſed; ſo that the pofition of the cups a and the largeneſs of the e-
clipfe are different, in different places, at the fame time: for the fame reafon al-
fo, the time of the beginning, middle, and end of a ſolar eclipſe is different
in different places.
The other way of confidering folar eclipfes is that invented by Kepler, it
ſuppoſes a ſpectator placed in the moon to view the difk of the earth, and
the progrefs of the ſhadow and penumbra of the moon thereon; as alſo the
motion of countries, cities, and towns, upon the diſk, cauſed by the rotation.
of the earth round its axis: by this rotation, every place upon the diſk would
appear to move either in the equator, or in one of its parallels: that is, in a
ftrait line, if the projection of thefe circles is in ftrait lines, as in the 79th fi-
gure of the firſt book; in elliptic curves, if the projection of thofe circles is in
fuch curves, as in the 78th figure of the first book, and in the 39th of this
prefent book: now in order to know of what kind the projection of the cir-
cles upon the diſk of the earth is, at the time of any eclipſe, we muſt know
the fun's place in the ecliptic, at that time: the projection of the
equator and
its parallels is in ftrait lines, only when the fun is in the equator: if the fun
is in north or fouth declination the projection of thoſe circles is in elliptic
curves, which deviate more or less from ftrait lines, according as the declina-
tion of the fun is greater or lefs: whatever the declination of the fun is, he is
vertical to the parallel which is at the like diſtance from the terreſtrial as the
39 fun is from the celeftial equator: thus, fig. 39, at the middle of the general
eclipſe of july the 14 1748, the fun was in 19°35′ north declination, conſe-
quently vertical to the parallel ACB of 19° 35′ north latitude; in that paral-
lel then at c muft the center of the difk be: the rectilinear meridian PC is
that which is then turned to the fun: how far that is eaſt or weft from the
meridian of Greenwich, muſt be known by having the time of the middle of
the eclipſe; which at Greenwich was 11h 23 in the morning; it was then
noon under the meridian PC: that meridian therefore is 37 in time, or 9° 15′
eaſt from the meridian of Greenwich.
1032 At the moment of the moon's conjunction with the fun, imagin part
of the ecliptic with the fun's place therein, and part of the moon's way from
40 the fun to be projected upon the plane of the diſk extended, figg. 40-46:
41 the projection of the arc of the ecliptic will be A D, of the fun's place E the
42 center of the diſk, the projection of the moon's way from the fun will be LP,
a Whilst an eclipſe of the fun is partial, the fun appears like the horned moon: the tips of the hons of
the fun are called the cufps.
the
Book III.
80
page 395.
A
L
49
46
P
53
E
P
F
A
H
D
a
d
b
b
47
B
14
48
50
A
9
h
ん
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51
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a
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1
+
}
і
52
A
B
N
M
L
54
P
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C
น
a
C
CHAP. 4.
395
ASTRONOMY
the projection of an arc of a fecondary of the ecliptic drawn from the eclip- FIC.
tic to the moon and meaſuring the moon's latitude will be EN: from the cen- 43
ter of the diſk E draw EM perpendicular to the way of the moon from the 44
fun, this will fhew where the center of the ſhadow and penumbra, when
45
the ſhadow reaches the earth, or the center of the penumbra only, when the 46
fhadow does not reach ſo far as the earth, is at the leaft diftance from the
center of the diſk: now when the center of the penumbra is at м is the time
of the middle of the eclipfe, if that new moon be ecliptical: the middle of the
eclipſe is before the time of conjunction, when the conjunction falls out af-
ter the moon has paffed her node, as fig. 42, 43; but after the time of con-
junction, when that falls out before the moon is come to her node, as fig. 44,
45: when the moon is in the node at the moment of her conjunction with
the fun, the time of the conjunction is the fame with the time of the mid-
dle of the eclipfe, fig. 46. How much the time of the middle of the eclipſe
is before or after the time of the conjunction may be known, by finding the
meaſure of the arc M N, and the time the moon takes to go through that arc in
her hourly motion from the fun. Aftronomers give us tables wherein is ſet
down the time the moon takes to go through the arc MN; this time is to be
added to or ſubtracted from the time of the true conjunction, in order to de-
termine the time of the middle of the eclipſe, and is different, according as
the velocity of the moon's motion from the fun and her diſtance from her
node are different: theſe tables, like thoſe mentioned § 1024, reach no far-
ther than the ecliptic limits.
The largeness of the earth's difk is thus found; the femidiameter of it is e-
qual to the horizontal parallax of the moon, § 980: from the center E draw
a circle at pleaſure to reprefent the difk, if the femidiameter thereof be
divided into as many parts as the horizontal parallax of the moon contains
minutes and ſeconds, it will ſerve for a ſcale by which the circles of the ſha-
dow and penumbra may be ſet off in their proper dimenfions: from the cen-
ter м draw a circle, taking from the fcale for its femidiameter as many mi-
nutes and feconds as the excefs of the apparent femidiameter of the moon a-
bove that of the fun amounts to, this will exhibit the circle of the moon's fha-
dow; from the fame center м draw a circle M н, taking from the ſcale its ſe-
midiameter equal to the fum of the femidiameters of the fun and moon, and
this will repreſent the circle of the penumbra, in its true dimenfions: theſe things
being done, if the diſtance Eм be greater than the ſum of the femidiameters
of the diſk and of the penumbra, as fig. 40, there can be no eclipſe; for
the penumbra will not touch the diſk: 2, if the diſtance be equal to that ſum,
as fig. 41, the penumbra will juſt touch the difk, but caufe no eclipfe: 3, if 41
40
EM
396
BOOK 3.
ASTRONOMY
FIG. EM be leſs than that fum, that is leſs than м H added to F в, but greater than
42 the fum of the femidiameters of the ſhadow and the diſk, as fig. 42, the pe-
numbra will cover fome part of the diſk; for example, in the middle of the
eclipfe, the fegment F G H B, and caufe to the inhabitants of thoſe parts of the
earth over which it paffes a partial eclipſe: 4, if the diſtance Eм be leſs than
43 the fum of the femidiameters of the ſhadow and the diſk, as figg. 43, 44, the
44 fhadow will cover fome part of the difk, and cauſe a total eclipfe of the fun
in all the places over which it paffes; which eclipfe will alſo be central in all
the places over which the center of the fhadow paffes.
1033 For the duration of folar eclipfes, take the following lemmata. If the
moon is in her node, the center of her fhadow paffes over the center of the
earth's enlightened diſk, and deſcribes a diameter thereof, which is the long-
eft line that can be drawn in a circle, as ab; if the moon has latitude, the cen-
ter of her ſhadow deſcribes a chord in the circular diſk of the earth, a line
47 leſs than a diameter, as cd, fig. 47.
1034 The beginning of the general eclipfe is when the penumbra of the moon
firſt touches the diſk of the earth; the end is when the penumbra leaves the
diſk: The duration of the general eclipfe is the time that paffes from the firſt
entrance of the penumbra upon the diſk till it is gone entirely off: all that
time the fun appears to be eclipfed in ſome part of the earth or other: the
duration of the general eclipfe depends upon 1, the velocity of the moon's
motion from the fun: 2, upon the length of the line deſcribed upon the diſk
of the earth by the center of the penumbra, 3, upon the largeneſs of the ſha-
dow and penumbra, 4, upon the largeneſs of the diſk of the earth: the diſk
of the earth is largeſt when the moon is in perigee, leaſt when in apogee. The
beginning of a folar eclipfe in any place is when the penumbra firſt touches the
place; the end when the penumbra leaves the place: the beginning of total
darkneſs in any place is when the ſhadow firft touches the place; the end when
the fhadow leaves it: all the time the penumbra is paffing over any place,
the eclipſe is partial in that place: all the time the fhadow is paffing over
any place, the inhabitants thereof have the fun totally eclipfed. It is eaſily
underſtood, that it is day in every place upon the enlightened diſk of the earth:
2, that when by the rotation of the earth any place comes firft into the diſk,
the fun appears then to rife in that place; 3, when any place is by the fame
rotation carried from off the diſk, the fun appears to fet in that place: 4, when
the meridian of any place comes to ſtand towards the fun, as the rectilinear
39 meridian pf does, fig. 39, it is noon in that place: hence it follows, that
where the penumbra firſt touches the diſk, the inhabitants of that place fee
the
CHAP. 4.
397
ASTRONOMY
the beginning of the eclipfe at fun-rife; where the penumbra laft leaves the FIG.
diſk, the inhabitants fee the eclipſe end when the fun is ſetting with them.
1035 In an eclipfe of the fun that is central and barely total in any place,
fince only the tip of the cone of the moon's fhadow reaches the place;
the ſhadow is ſo ſmall that it is no fooner upon the place than it is off again:
to the inhabitants of that place, the fun appears to be entirely covered by the
moon, for a moment only; fuch an eclipfe is faid to be total without ftay: an
eclipſe may alſo be without ftay, though the ſhadow be of fome breadth, if
the place be fo fituated that a line drawn through it upon the difk of the earth
parallel to the way of the center of the fhadow only touches one edge of the
Thadow. In an eclipse of the fun that is more than total in any place, the
fhadow of the moon takes up fome time in paffing over that place; fuch an
eclipfe is faid to be total with ſtay: the time of ſtay or total darkneſs in any
place is the time the fhadow is paffing over it: this time is variable from the
different length of the diameter or chord of the fhadow that paffes over the
place, and the different velocity of the moon's motion from the fun, § 958.
1036 In fig. 48, let fgb be the earth, cde part of the orbit of the moon; 48
for fo little a time as the ſhadow and penumbra are paffing over the diſk of
the earth in the direction fg, we may, without fenfible error, confider the
motion of the moon as if it were in a ftrait line, in the direction ab: in which
cafe the axis of the ſhadow would be carried parallel to it ſelf; and confequent-
ly, the velocity of the center of the fhadow in the direction fg would be equal
to the velocity of the moon in the direction ab: the moon goes through her
orbit of 360 degrees in 29 days and an half; that is, at the rate of about one
degree in 2 hours. Since the femidiameter of the moon's orbit is equal to 60
femidiameters of the earth, § 980; one degree in the orbit of the moon is
equal to 60 degrees of a great circle upon the furface of the earth: therefore
the moon's ſhadow and penumbra go upon the diſk of the earth at the rate
of 60 degrees or 3600 geographical miles in two hours, that is, 30 fuch miles
in a minute of an hour; which is about three times as ſwift as the motion of
a cannon ball when it firſt leaves the mouth of the cannon, according to ex-
periments related in the hiſtory of the R. Academy of Sciences at Paris for
the year 1706. The diameter of the fhadow being finall, and the motion
thereof thus ſwift, any place over which it paffes is quickly out of the ſha-
dow into the penumbra; therefore the total darkneſs in any place, even where
the eclipſe is central, continues but a few minutes, § 1044: the diameter of
the penumbra, being pretty large, is a confiderable time in paffing over any
place which lies near the way of its center; and therefore, in a place fo fitu-
ated, the partial eclipfe may laſt above two hours.
3 E
1037
398
BOOK 3.
ASTRONOMY
FIG.
1037 Let meridians be projected upon the enlightened diſk of the earth
49 through every 15th degree of the equator, as in fig. 49, where an is the e-
quator, the elliptic curves pas, pbs, &c and the ſtrait line pgs are meridi-
39 ans; in this projection, as alſo in that of the 39th figure, the parts of the
earth are exhibited larger the nearer they are to the center of the difk; leſs,
the nearer they are to the circumference: thus, the meridians are more di-
itant from each other the nearer they are to the rectilinear one which is drawn
through the middle of the difk: from hence it follows, that the axis of the
moon's fhadow, being carried nearly parallel to it felf during the time of a
folar eclipſe, ſo as to defcribe equal lines in equal times upon the earth's diſk,
will deſcribe unequal lines in equal times upon the ſpherical ſurface of earth:
let the center of the fhadow move equably over the difk of the earth in the
49 line abcdef&c, according to the order of the letters, fig. 49; it will then paſs
from a to d, or from k to n, that is, through three meridians 15 degrees a-
funder, nearly in the fame time as it goes from ƒ tog, or from g to b, which
is only from one meridian to another that is but 15 degrees diſtant from it:
thus we ſee the ſhadow and penumbra is longer in paffing over any place, the
nearer that place is to the center of the diſk.
1038 If an eclipſe of the fun be confidered as it appears in the heaven, the
moon's motion from the fun being generally eastward, the beginning of a fo-
lar eclipfe in any place is when the eaſtern edge of the moon's diſk, ſeen from
that place, firſt appears to touch the weſtern edge of the fun's difk; the end
of the eclipfe is when the weſtern edge of the moon's diſk appears to leave the
eaſtern edge of the fun's difk: the duration of a ſolar eclipfe in any place is all
50 the time the moon appears to cover any part of the fun: in fig. 50, let AB
be part of the apparent orbit of the moon, s the fun, м the center of the moon
at the beginning, N her center at the end of the eclipſe, the duration of the e-
clipſe is the time the moon, in her motion from the fun, takes in paffing from
M to N ; that is, in a central eclipfe, through an arc equal to the fum of the ap-
parent diameters of the fun and moon: the apparent diameter of the moon in
apogee, when her motion is floweft, is 29′ 30″, the apparent diameter of the
fun when greateft 32′ 44″, the ſum of theſe two diameters is 62′ 14″: when
the luminaries are in theſe circumftances, which are fuch as make a folar e-
clipſe of the longest duration, the moon in fyzygy goes in her motion from
the fun at the rate of 27 4" in an hour, which carries her through an arc of
62′ 14″ in 2 hours and 18 minutes: and this would be the longeſt duration
poffible of an eclipſe of the fun, if it were feen from the center of the earth.
Scholium. The eclipſe now deſcribed muſt be annular, becauſe the appa-
rent diameter of the moon is less than that of the fun; fo that there would be
no
CHAP. 4.
399
ASTRONOMY
no total darkneſs. If the luminaries be both in perigee, the apparent diame- FIG.
ter of the moon in the horizon is then 33′ 38″, of the fun 32 44", the fum of
thefe is 66′ 22″: fuch an eclipfe will be greater, than when the moon is in
apogee, becauſe the moon will now more than cover the whole fun; but the
duration of it will be ſhorter; becauſe the greater velocity of the moon in pe-
rigee more than compenfates for the greater length ſhe has to go, between the
beginning and end of the eclipfe.
any
When the eclipfe begins in any place it is partial, and continues fo all the
time the moon appears to advance over the diſk of the fun, covering more
and more of it every moment, till the whole diſk is hid; if the place be fo
fituated as to have a total eclipſe, at that time: the eclipſe can be total in
place but for a few minutes only, as has been faid before; when the time of
total darkneſs is over, the leaft thread of light, that comes directly from that
edge of the fun's difk which is first left by the moon fuddenly illuminates
the air to a degree that appears furprizing; efpecially if the darkneſs has laſt-
ed 2 or 3 minutes, fo as to dilate the pupils of the eyes of the ſpectators: the
eclipfe is then again partial, and continues fo, gradually decreafing, as the
noon paffes off from the diſk of the fun, and every moment lets more and
more of him be ſeen, till his whole difk is again vifible in that place. When
an eclipfe is only partial in any place, the moon appears every moment, after
the beginning, to cover more and more of the fun, till the time of the mid-
dle of the eclipfe, or greateft obfcuration; then the eclipfe gradually decreaſes,
the moon continually letting more and more of the fun be feen, till the
eclipfe is over, in that place: of the duration of partial eclipfes I fhall
treat hereafter.
1039 The beginning of total darkneſs in any place is when the moon firſt
appears to a ſpectator in that place to cover the whole diſk of the fun; the
end of total darkneſs in any place is when the moon by her motion from the
fun, lets fome part of his difk be feen again, in that place. The duration of
total darkneſs in any place is all the time the diſk of the fun appears to a ſpec- 51
tator in that place to be entirely covered by the moon: in fig. 51, let MN be
part of the apparent orbit of the moon, ac the apparent diameter of the moon,
be the apparent diameter of the fun, the figure repreſents the moon juft co-
vering the whole diſk of the fun, as fhe appears to do at the beginning of to-
tal darkneſs: this darkneſs continues till a the weſtern edge of the moon's
diſk appears to go from a to b the weſtern edge of the difk of the fun: the
duration then of total darkneſs is while the moon in her motion from the
fun, is going through an arc of her apparent orbit equal to ab, the exceſs of
the moon's apparent diameter above the apparent diameter of the fun.
3 E 2
1040
400
BOOK 3.
ASTRONOMY
FIG.
when
1040 The apparent diameter of the moon in the horizon in ſyzygy
in perigee is 33′ 38", by the tables: of the fun in apogee is 31′ 38″, §
775: fo that the apparent diameter of the moon in fyzygy in the horizon
when greateſt does not exceed the apparent diameter of the fun when
that is leaſt above two minutes of a degree: in this fituation of the lumina-
ries, as appears by the tables of the hourly motions of the fun and moon, the
motion of the moon from the fun is 35 48" in an hour, which is at the rate
of 2 minutes of a degree in 3 minutes and about 20 feconds in time; this
then would be the longeft poffible duration of total darkness, even when an e-
clipfe of the fun is central, if it were viewed from the center of the earth:
this alfo would be the longeſt duration of a folar eclipfe, when the luminaries
are in the horizon, if the place of the fpectator were a fixt point. The du-
ration of total darkneſs in a central eclipfe depends not upon the exceſs of the
that
apparent diameter of the moon above that of the fun alone, but upon
exceſs and the velocity of the moon's motion from the fun confidered toge-
ther: this exceſs is increaſed by the moon being in the zenith in a greater ra-
tio than the apparent velocity of the moon is: therefore, the total darkneſs
will be of longer duration where the luminaries are in the zenith than where
they are in the horizon: thus, fuppofe the excess of the moon's apparent
diameter above that of the fun to be 2 minutes of a degree, as it is when the
fun is at the greateſt and the moon at the leaſt diſtance from the earth; this
exceſs, when the moon is in the zenith, being increaſed a 60th part of 33′
38″ her apparent diameter, will amount to a little more than 2' 33"; fo that
the exceſs is about a 4th part greater in the zenith than in the horizon; but,
the apparent velocity being increaſed only a 60th part, the duration of total
darkness is I
longer in the zenith than in the horizon: thus, if in the ho-
rizon the total darkneſs were 3' of an hour, to a ſpectator who has the lumi-
naries in his zenith it would be 3' 42': it is very eafy to conclude from hence
that the duration of total darkneſs in any folar eclipſe is longer in any place
the nearer the luminaries are to the zenith of that place during the time of
total darkneſs.
1041 When the moon is in the zenith of any place, he is a femidiameter of
the earth or about a 60th part of her whole diſtance, nearer to that place
52 than in the horizon, thus, fig. 52, let a fpectator be upon the earth at a,
if the moon be in his fenfible horizon at B, her diftance from A is very near-
ly the fame as from c the center of the earth; if the moon be in his zenith
at z, her diſtance is then no more than az, which is leſs than CB by AC,
that is by a whole femidiameter of the earth; or about a 60th part of her
whole diſtance: now, fince the apparent diameter of a globe increaſes in the
fame
CHAP. 4.
401
ASTRONOMY
fame ratio as its diſtance from the eye is diminiſhed, § 242, 243, the appa- FIG.
rent diameter of the moon in the zenith is about a 60th part greater than in the
horizon: it is eaſy to ſee that as the moon rifes from the horizon towards the
zenith ſhe approaches nearer to the eye of the ſpectator, and confequently
her apparent diameter continually increaſes: in the table at the end of the
prefent chapter, may be ſeen how much the apparent diameter of the moon
increaſes as the goes from the horizon towards the zenith, for every five de-
grees of her altitude. The fun's diſtance is fo great, that his being a ſemi-
diameter of the earth nearer will not fenfibly increaſe his apparent diame-
ter; therefore eclipſes of the fun are, cæteris paribus, greateſt in thoſe places
where the luminaries are neareſt the zenith: for, whereas the fun continues
of the fame diameter, he is covered by a moon of greater diameter, the near-
er the luminaries are to the zenith.
1042 The apparent motion of the moon is fwifter the nearer ſhe is to the ze-
nith of any place: this increaſe of the apparent velocity of the moon is in
the ſame ratio as the increaſe of her apparent diameter: for this reaſon, a
tranfit of the moon over a ſtar which appears but as a point would take
up the
fame time whether the moon be in the horizon or the zenith, if the place of
the ſpectator were at reſt; the greater apparent diameter of the moon in the
zenith being balanced by her proportionally greater apparent velocity. Thus
in fig. 53, let AH be the earth, BDG the orbit of the moon, BC the apparent 53
diameter of the moon in the horizon, fuppofe it of 33'; take D E equal to B C:
if DE be viewed by a ſpectator at a in his zenith, it will appear to fubtend an
angle of 33′ 33″, a 60th part greater than BC does viewed from н the center
of the earth, or from A in the horizon of the ſpectator: for BC feen from н is
meaſured in the circle BDG, the femidiameter of which is H.B; but DE feen
from A is meaſured in the circle EFL, the femidiameter whereof is AD, leſs-
than H B. by a 60th part: now if each of theſe circles be divided into degrees
minutes and ſeconds, the degrees minutes and ſeconds contained in BC mea-
fured in the circle BCG muſt be as much larger than thoſe of DE meaſured
in the circle DE F, as H B is greater than AD; for the peripheries of circles or
fimilar arcs of them are as their femidiameters, and confequently, the number
of feconds in DE thus meaſured muſt be to the number of ſeconds in BC reci--
procally as their magnitude: fo that if 1980 the number of ſeconds in BC be-
divided into 60 parts, there will be one of thoſe parts or about 33" in DE more:
than in BC. Again, if B C and DE be confidered as equal arcs which the moon:
goes through in a given time, it is eaſy to ſee that the angular motion of the
moon through DE feen from A is a 60th part greater than that through BC.
feen from н or from A: for, from A the motion of the moon through DE ap-
pears
402
BOOK 3.
ASTRONOMY
FIG. pears to be through an arc of about 33 feconds more than the arc в C appears
53 to contain, viewed from H or A. So that if, for inftance, the moon ſeen from
H or A appears to go through B C an arc of 33′ in a given time, ſhe will, ſeen
from A, appear to go through DE an arc of 33′ 33″, in the ſame time.
1043 The duration of a central folar eclipfe in any place depends upon the ap-
parent velocity of the moon's motion from the fun and the fum of the appa-
rent diameters of the fun and moon confidered together: the increaſe of this
fum, as the luminaries are feen nearer to the zenith, arifes from the increafe
of the apparent diameter of the moon only, for the fun's apparent diameter
is not fenfibly increaſed: the apparent diameter of the moon is nearly equal
to that of the fun: the increaſe therefore of a 60th part in the moon's
appa-
rent diameter will increaſe the fum of the apparent diameters of both lumi-
naries only an 120th part of that fum: the apparent velocity of the moon in
the zenith is a 60th part greater than in the horizon; but, allowing for what
is balanced by the increaſe of the fum of the apparent diameters, we may
confider the increafe of the apparent velocity as being only an 120th part,
the effects are the fame as if it were ſuch, the duration of a ſolar eclipſe will
be an 120th part fhorter in the zenith than in the horizon: thus, an eclipfe,
which in the horizon would laſt 2 hours, will, if ſeen in the zenith, laſt but
1 hour and 59 minutes.
1044 We have hitherto confidered what would be the longeſt duration
of a folar eclipfe viewed from the center of the earth, or from the furface,
fuppofing the earth had no rotation round its axis: but, as every place upon
the furface of the earth is, by this rotation, carried round nearly the ſame
way that the moon goes in her orbit, this motion of the place of a ſpectator
will cauſe the motion of the moon to appear to him ſo much flower as his
own motion amounts to, than it would do if he were to view it from a fixt
point: if the ſpectator be at the equator, and in the middle of the diſk, he is
carried with greater velocity the fame way with the moon than on any other
part of the earth; the motion of any point of the equator is at the rate of 15
geographical miles in a minute, which is very little leſs than half of the
moon's motion from the fun, in the caſe we are now fuppofing, when that
motion is ſwifteft of all: ſo that, the diameters of the luminaries being as
was mentioned § 1040, in a folar eclipfe that happens when they are in
the zenith, the time of total darkneſs is by the rotation of the earth increaſed
almoſt half, and may amount to about five minutes of an hour. If
the ſpectator be upon the equator and near the edge of the diſk, the rotation
of the earth carries him round with the fame velocity as in the cafe juft now
mentioned; but, becauſe a line drawn from the moon to his place is then ve-
ry
CHAP. 4.
403
ASTRONOMY
ry nearly a tangent to the earth, the rotation carries him almoft directly to- FIC.
wards the moon, or almoft directly from her; but his motion the fame way
with the moon is then fo little as to be ſcarcely fenfible: in this caſe, the ro-
tation of the earth contributes very little towards lengthening the duration of
total darkneſs: it will therefore be very nearly the fame as if the eclipſe were
viewed from the center of the earth. In fig. 54, let м be the moon, LMN
54
be part
of the orbit of the moon in which the moves according to the order
of thoſe letters, abcd the equator of the earth, P one of the poles: by the
earth's rotation according to the order of the letters, the fame way with the
moon, a fpectator upon the earth at a who has the moon in his zenith con-
tinues the longer in the fhade, becauſe he is carried along with it, as it moves
the earth from a towards b; whereas a fpectator at d who has the moon
in his horizon, being carried almoft directly towards M, may be confidered as
ftationary in reſpect of the moon; as may a fpectator alfo at b, who is carried
almoſt directly from the moon.
upon
Corol. The time of total darkneſs in any place is more or lefs increaſed by
the rotation of the earth, according as that place is near to the equator or
diſtant from it, and has the luminaries nearer to or farther from the zenith at
the time of the middle of the eclipfe. The rotation of the earth lengthens alſo
more or leſs the time the fun is partially eclipſed in any place, in the fame man-
ner as it does the time of total darkneſs in that place: in an eclipſe that is
central or nearly fuch, if the ſpectator be near the equator, and has the lu-
minaries near his zenith, the rotation of the earth will lengthen the duration
above half an hour.
1045 The darkness in a total eclipse of the fun may be diminiſhed, 1, by
fome of the light of the fun refracted through the atmoſphere of the moon;
2, by the light of the fun's atmoſphere: 3, by that light which extends it ſelf
from the fun both ways along the ecliptic, deſcribed by Dam. Caffini in a trea-
tife upon that fubject, whereof I fhall give an account in a proper place: 4,
by the fun's light falling upon thofe parts of our atmoſphere which, though
not within our view, are near enough to us to reflect that light upon fome
parts of our atmoſphere that are within our vifible horizon. The circle of
pale light that appears round the moon in a total eclipſe of the fun is with
great probability fuppofed to be owing to the atmosphere of the moon: total
eclipſes of the fun wherein this pale light has been ſeen have ſometimes, by
miſtake, been thought to be annular, when the tables of the fun and moon
have made it manifeft that the apparent diameter of the moon was not at
thoſe times leſs than that of the fun; as it muft neceffarily be to caufe an.
annular eclipſe.
1046
404
ASTRONOMY
BOOK 3.
any at-
1046 It has been difputed among aftronomers, whether the moon has
mosphere or not: to prove the has none, it is alledged that, in an appulfe of
the moon to a ſtar, when ſhe comes fo near to it that part of her atmoſphere
is interpofed between our eye and the ftar, refraction would cauſe the ſtar to
feem to change its place, fo that the moon would appear to touch it later
than by her own motion fhe would do: the anfwer to this is, that the atmo-
ſphere of the moon, having but a third part of the denſity of the earth's at-
moſphere, is too thin to produce fuch refraction of the ftar as to cauſe a vifi-
ble change of its place in the heaven. Sir Ifaac Newton has fhewn, princip.
prop. 37, cor. 5, that the weight of any body upon the moon is but a third
part of what the weight of the fame would be upon the earth: now the ex-
panfion of air is reciprocally as the weight that compreffes it; the air there-
fore furrounding the moon being preffed together by a weight, or being at-
tracted towards the center of the moon by a force, which is equal but to a
third part of the force with which our air is attracted towards the center of
the earth, our atmoſphere muſt be three times as denfe as the atmoſphere of
the moon. Some philofophers are of opinion that there are no feas or lakes
in the moon, and from thence conclude there is no atmoſphere, becauſe there
is no water there to be raiſed up in vapours: I have before fhewn that it is
very probable ſome of the dark ſpots upon the moon are water, and given an
anfwer to the arguments which are brought to prove the contrary, § 965.
1047 Though we have mention made in ſeveral paffages of ancient and
later hiftorians of the fun being, at different times, fo darkened by the inter-
pofition of the moon that the day ſeemed to be turned into night, and that
the ſtars appeared, as may be feen in the catalogue of eclipfes given by Ric-
ciolus in his Almagest l. 5. c. 19; yet have we no good deſcription of any to-
tal eclipſes of the fun, till we come to thoſe which have happened in the
prefent century; and theſe, eſpecially fuch as were total in any part of Eu-
rope, have been obferved by divers able aftronomers with fuch attention, that
it will be worth while to lay before the reader fome extracts from the ac-
counts of them which have been made public.
In the eclipſe may the 1ft 1706, Captain Stanyan from Bern in Switzer-
land writes, that 'the fun was totally darkened there, for 4 minutes and of
44
'time; that a fixt ſtar and a planet appeared very bright, that his getting out
'of the eclipfe was preceeded by a blood-red ftreak of light, from his left
'limb, which continued not longer than 6 or 7 feconds of time; then part of
'the fun's disk appeared, all on a fudden, brighter than venus was ever ſeen
in the night, and in that very inftant gave light and ſhadow to things as
'ſtrong as moon light uſes to do.' The publiſher of this account obſerves that
the
CHAP. 4.
405
ASTRONOMY
the red ftreak of light preceeding the emerfion of the fun's body infers that
the moon has an atmoſphere; and its ſhort continuance of 6 or 7 feconds tells
us that its height is not more than the 5 or 6 hundredth part of her diameter.
The fame eclipſe was obſerved at Geneva by Fatio, who fays 'there was
'feen, during the whole time of the total immerfion, a whiteness, which
'feemed to break out from behind the moon, and to encompaſs her on all
'fides equally: this whiteness was not well defined on its outward fide, and
'the breadth of it was not a twelfth part of the diameter of the moon.
"This planet appeared very black, and her diſk very well defined, within the
'whiteness which encompaffed it about, and was of the fame colour as that
'of a white crown or Halo of about 4 or 5 degrees in diameter, which accom-
'panied it and had the moon for its center. A little after the fun had
'begun to appear again, the whiteness and the crown which encompaſſed the
'moon did entirely vaniſh.' I muſt add, that this deſcription is a little perplext
either through the fault of the author or of the tranflator; for I fuppofe Fa-
tio wrote in French; however it plainly appears by it, that the moon's at-
moſphere was vifible, furrounded by a light of larger extent, which I think
muſt be that luminous appearance mentioned from Caffini, § 1045. Flamsteed
who publiſhed this account takes notice that, according to theſe obſervations,
the altitude of the moon's atmoſphere cannot be well fuppofed lefs than 130
geographical miles: and that probably this atmoſphere was never diſcovered,
before this eclipfe, by any refraction of the ſtars, by reafon of the fmallneſs
of the refraction, and for want of proper obfervations.
Dr. Scheuchzer's account of the fame eclipfe as feen at Zurich is in theſe
words, 'we had an eclipſe of the fun which was both total and annular: to-
'tal, becauſe the whole fun was covered by the moon; annular, not what is
'properly fo called, but by refraction; for there appeared round the moon a
"bright ſhining, which was owing to the rays refracted through the atmoſphere
'of the moon. Phil. tranfact. n. 306.
1048 Dom. Caffini, who had tranfmitted to him obfervations of this eclipſe
from feveral places, gives a large account of it, in a memoire of the year
1706 he fays that, in all thofe places where it was total, during the
time of total darkneſs, there was feen round the moon a crown, or broad
circle of pale light, the breadth whereof was about a 12th part of the moon's
diameter: that at Montpellier, where the obfervers were particularly attèn-
tive to ſee if they could diſtinguiſh the luminous path in the zodiac mentioned
§ 1045, they took notice of a paler light of a larger extent, which furround-
ed the crown of light before mentioned, and ſpread it ſelf on each fide of it,
to the diſtance of four degrees. He then mentions Kepler's opinion, that the
3 F
crown
406
воок 3.
ASTRONOMY
crown of light which appears round the moon during the total darkneſs in
an eclipſe of the fun is cauſed by ſome celeſtial matter furrounding the moon,
of fufficient denfity to receive the rays of the fun, and fend them to us, and
that the moon may have an atmoſphere fimilar to that of our earth, which
may refract the rays of the fun: he tells us that he (Caffini) had often obſer-
ved occultations of faturn, of jupiter and his fatellits, and of fome fixt ſtars,
cauſed by the moon, without perceiving any change in thoſe ftars, at their
immerfion; which made him imagin there was at that time no atmoſphere
on that fide of the moon which hid them: but, at other times, a ſtar has ap-
peared to change its place a little, immediately before the appulfe of the moon,
whether that were on her bright or dark fide: and that this induced him to
be of opinion that, there was, at thoſe times, on that fide of the moon, fome
matter, denſe enough to refract the light of the ftars, and cauſe thoſe appear-
ances.
1049 In the
year 1715, on the 22d of april old ſtyle, there was an eclipſe
of the fun, which, being total at London, was obſerved there by Halley, ac-
companied, befides many others, by Louville of the R. Academy of Paris who
came into England for that purpoſe. I ſhall give fo much of Halley's account
of it as I think neceffary, in his own words.
'It was univerfally obferved, that when the laſt part of the fun remained
'on his eaft fide, it grew very faint, and was eaſily ſupportable to the naked
'eye, even through the teleſcope, for above a minute of time before the to-
'tal darkneſs; whereas, on the contrary, my eye could not endure the ſplen-
'dour of the emerging beams in the teleſcope from the firſt moment. To this
'perhaps two cauſes concurred; the one, that the pupil of the eye did necef-
'farily dilate it ſelf during the darkneſs, which before had been much con-
"tracted by looking on the fun. The other, that the eaſtern parts of the
'moon, having been heated with a day near as long as thirty of ours, muſt of
'neceffity have that part of its atmoſphere replete with
of its atmoſphere replete with vapours, raiſed by the
'fo long continued action of the fun; and by confequence, it was more denſe
'near the moon's furface, and more capable of obftructing the luftre of the
'fun's beams. Whereas at the fame time the weſtern edge of the moon had
'fuffered as long a night, during which there might fall in dews all the va-
'pours that were raiſed in the preceding long day; and for that reaſon, that
'part of its atmoſphere might be ſeen much more pure and tranſparent.
‘About two minutes before the total immerfion, the remaining part of the
'fun was reduced to a very fine horn, whoſe extremities feemed to looſe their
"acuteness, and to become round like ſtars. And for the ſpace of about a
'quarter of a minute, a fmall piece of the fouthern horn of the eclipſe feem-
ed
CHAP. 4.
407
ASTRONOMY
'ed to be cut off from the reſt by a good interval, and appeared like an ob-
'long ſtar rounded at both ends: which appearance could proceed from no o-
'ther cauſe, but the inequalities of the moon's furface, there being fome ele-
'vated parts thereof near the moon's fouthern pole, by whofe interpofition,
'part of that exceedingly fine filament of light was intercepted.
'A few feconds before the fun was totally hid, there diſcovered it ſelf round
'the moon a luminous ring, about a digit or perhaps a tenth part of the
'moon's diameter in breadth. It was of a pale whiteneſs, or rather pearl co-
'lour, feeming to me a little tinged with the colours of the Iris, and to be
'concentrick with the moon; whence I concluded it the moon's atmoſphere.
'But the great height of it, far exceeding that of our earth's atmoſphere; and
'the obfervations of fome who found the breadth of the ring to increaſe on
'the weft fide of the moon, as the emerfion approached; together with the
'contrary fentiments of thoſe, whoſe judgment I ſhall always revere, makes
'me lefs confident, eſpecially in a matter whereto I gave not all the attention
requifite.
'Whatever it was, this ring appeared much brighter and whiter near the
'body of the moon, than at a diſtance from it; and its outward circumference,
'which was ill defined, ſeemed terminated only by the extream rarity of the
"matter it was compofed of; and in all refpects reſembled the appearance of
'an enlightened atmoſphere viewed from far: but whether it belonged to the
'fun or moon, I ſhall not at prefent undertake to decide.
'During the whole time of the total eclipfe, I kept my teleſcope conſtant-
❝ly fixt on the moon, in order to obſerve, what might occur in this uncom-
'mon appearance, and I faw perpetual flaſhes or corrufcations of light, which
'feemed for a moment to dart out from behind the moon, now here, now
'there, on all fides, but more eſpecially on the weſtern fide, a little before
'the emerfion: and about two or three feconds before it, on the fame weſtern
*fide, where the fun was juſt coming out, a long and very narrow ſtreak of
'a duſky, but ſtrong red light, ſeemed to colour the dark edge of the moon,
"though nothing like it had been ſeen immediately after the immerfion. But
'this inftantly vaniſhed upon the first appearance of the fun, as did alſo the
'aforefaid luminous ring. Phil. tranfact. n. 343.
1050 Louville, giving an account of this eclipfe a, mentions, as one of the
principal things taken notice of, a luminous ring of a filver colour that ap-
peared round the moon, affoon as the fun was entirely covered by her diſk,
and diſappeared the moment he recovered his light: that this ring was bright-
eft near the moon, and grew gradually fainter towards its outward circumfe-
3 F 2
a Memoires d'Acad. annee 1715.
rence
408
ASTRONOMY
воок 3.
rence, where it was however defined: that it was not every where alike
bright, but had ſeveral breaks in it: he makes no doubt of its being cauſed
by the moon's atmoſphere, and thinks the breaks obſerved therein were ow-
ing to the mountains in the moon: he fays the ring was exactly concentric
to the moon not to the fun, during the whole time of its appearance. Another
proof brought by him of the moon having an atmoſphere is that, towards the
end of total darkneſs, there was feen on that fide of the moon on which the
fun was going to appear a piece of a circle of a lively red, which might be
owing to the red rays, that are leaſt refrangible, being tranſmitted through
the moon's atmoſphere in the greateſt quantity: and, that he might be affu-
red this redneſs did not ariſe from the glaffes of his teleſcope, he took care to
bring this red part into the middle of thoſe glaſſes.
Louville lays a great ſtreſs on the ſtreaks of light which he ſaw dart inftan-
taneouſly from different places of the moon, during the time of total dark-
nefs; but chiefly near the eaſtern edge of her diſk: theſe he takes to be light-
nings, fuch as a ſpectator would fee flaſh from the dark hemifphere of the
earth, if he were placed upon the moon, and faw the earth come between
himſelf and the fun: now it is highly probable that, if a man had at any time
a view of that half of the earth where it is night, he would fee lightning in
fome part of it or other; he farther obferves that the moſt mountainous coun-
tries are moſt liable to tempefts, and that, mountains being more numerous
on the moon and higher than on the earth, thunder and lightning muſt be
more frequent there than with us: and that the eaſtern fide of the moon
would be moſt ſubject to thunder and lightning, thoſe parts having been heat-
ed by the fun for the half month immediately preceeding. I muſt here take
notice that Halley, in mentioning theſe flaſhes, fays they ſeemed to come from
behind the moon; that Louville, though he fays they came fometimes from
one part of the moon and fometimes from another, owns that he himſelf
faw them only near the eaſtern fide of her diſk, and that, not knowing at that
time what it was he ſaw, he did not think of taking notice whether the
fame appearance was to be ſeen in other parts of the moon or not; and wiſh-
es this phenomenon may be attended to in total eclipſes of the fun which
ſhall be obſerved hereafter. He tells us of an Engliſh aſtronomer who pre-
fented the Royal Society with a draught of what he ſaw in the moon at the
time of this eclipſe; from which draught Louville feems to conclude that a-
ſtronomer had obferved lightnings near the center of the moon's diſk: now
thunder and lightning would be a demonftration of the moon having an at-
mofphere of a nature fimilar to ours, wherein vapours and exhalations may
rife and be ſupported, and ſupply the materials for clouds, ſtorms and tempeſts.
But
page 409
N
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Book III.
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OF
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81
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X
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W* S. Sc.
CHAP. 4.
409
ASTRONOMY
But the ſtrongeſt proof brought by Louville of the moon having an atmo-
fphere is this, that, affoon as the eclipfe begun, thofe parts of the fun which
were going to be hid by the moon grew ſenſibly paliſh as the moon came near
them, fuffering beforehand a kind of imperfect eclipſe or diminution of light;
this could be owing to nothing elſe but the atmoſphere of the moon, the
eaſtern part whereof going before her reached the fun before the moon did.
As to the great height of the atmoſphere of the moon, which, from the
breadth of the luminous ring being about a whole digit, would upon a cal-
culation come out 180 miles, above 3 times as high as the atmoſphere of the
earth, Louville thinks that no objection; fince, if the moon were furrounded
by an atmoſphere of the fame nature with that which encompaſſes the earth,
the gravitation thereof towards the moon would be but a third part of that
of our atmoſphere towards the earth, and conſequently its expanſion would
make the height of it 3 times as great from the moon as the height of our at-
moſphere is from the earth, by what was faid § 1046. See the remarks.
1051 It has already been mentioned that, in an appulfe of the moon to a
ftar, the ſtar does not appear to change its place, upon the ſuppoſed atmoſphere
of the moon coming between the ſtar and our eye: that the fact is fo is rela-
ted in almoſt all the accounts we have of appulfes of the moon either to ſtars
or planets; though that there are fome exceptions to this general rule, may
be feen § 1048: to this we may add an obſervation made by Mr. Kirch at
Berlin, fept. 19, 1730, with a teleleſcope of 18 feet, of an occultation of ve-
nus by the moon: he fays that venus was then almoft in quadrature, and
that when ſhe came near the diſk of the moon, ſhe changed her ſhape, and,
the points of her horns diſappearing, became of an oval or elliptic figure:
which appearance he thinks is a proof that the moon has an atmoſphere. Phil.
tranſact. n. 412. See alſo what was faid § 1046, about the thinneſs of the
moon's atmoſphere.
1052 In the folar eclipſe of may the 11, 1724, the luminous ſtreaks men-
tioned § 1050, were not obſerved at Paris or Trianonª, though the eclipſe
was total in both thoſe places for above 2 minutes, and, at the laſt mention-
ed place, the obſervers Maraldi and Caffini were particularly attentive to that.
circumſtance: but they faw the ring of pale light as in former eclipſes.
To the preceeding accounts may added, that whereas, in the total eclipfes
of the fun of 1706 and 1715, a red light was viſible on the weft fide of the
moon juſt before the end of total darkneſs; the like phenomenon was ſeen in
the annular eclipſe of feb. 18, 1737, immediately before the ring was com-
pleated, and immediately after the eclipſe ceaſed to be annular. Ph.tranf.n.447.
4
a 'Memoires d'Acad. armee 1724.
Plutarch
410
BOOK 3.
ASTRONOMY
TIG.
Plutarch, in his treatife de facie in orbe lunæ, has a paffage which fhews
that the luminous ring round the moon in a folar eclipſe was taken notice of
by fome of the ancients: his words are thefe, Ariftarchus demonftrates the
ratio of the earth's diameter to that of the moon to be leſs than 60 to 19,
'greater than 108 to 43: from whence it comes to pafs that the earth, by rea-
❝ſon of its magnitude, deprives us of the fun, the whole night; but when the
'moon even hides the whole fun, it is without ftay, and without any extent,
(he argues as Kepler fuppofes from the obfervation of fome particular eclipfe which
had been fo circumftantiated) but there appears round her difk a brightneſs
'which hinders the darkneſs from being perfectly without any mixture of
light.
1053 There is one particular more, obfervable in eclipſes of the fun, that
whilft any part of the fun is covered by the moon, the diameter of the moon
appears leſs than it ought to do, according to her place in her orbit, and her
diſtance at that time from the earth: the French memoires ann. 1737, tell us
that, in a ſolar eclipſe 1684, the diameter of the moon appeared under an an-
gle of 305 at the moft; whereas, by obfervations made fome days before and
after the eclipfe, her diameter was found to be 31 30": fee alfo Phil. trans. n.
163. That luminous bodies appear under a larger angle than opake ones of
the fame dimenfions, and at the fame diſtance from the eye was mentioned
in note b§ 585. In the ſeveral phaſes of the moon wherein the dark part of
her is vifible, the luminous part appears a portion of a larger circle than the
dark part does: in the annular eclipfe of 1737, the ſmallneſs of the moon's
diſk upon the fun was furprizing to the fpectators: the refraction of the
moon's atmoſphere and the inflection of the rays of light ſpoken of § 220 may
both contribute to this appearance.
1054 The duration of total darkneſs has been fufficiently treated of: the
whole duration of a central folar eclipse, when all things concur to make it
the longeſt poffible, may be above 2 hours and 3 quarters, by § 1038, and
corol. of § 1044: it is obvious that the duration of a partial eclipſe of the fun
will be longer the nearer the circumſtances of it approach to thoſe of ſuch a
central one as was laſt mentioned. Where an eclipſe of the fun is central,
the diameter of the penumbra paffes over the place: where an eclipſe is total
but not central a chord of the ſhadow paffes over the place: where an eclipſe
is partial a chord of the penumbra paffes over the place: the duration of a
partial eclipſe depends upon the velocity of the moon's motion from the fun,
found by the tables, and the length of the chord of the penumbra that paffes
55 over the place. In fig. 55, let ENFS be the diſk of the earth, abfe the pe-
numbra of the moon, thofe places of the earth which lye under the line AB
have
CHAP. 4.
411
ASTRONOMY
have the diameter of the penumbra ab paſs over them, thofe under the line FIG..
CD are paffed over by the chord cd, thoſe under the line EF by the chord ef. 55
If partial eclipfes of the fun be confidered as they appear in the heaven, they may
be repreſented by figg. 56, 57; wherein let HR be the fun, NC the ecliptic, 56
XR the moon at the beginning, YH the moon at the end of the eclipfe, LP the
57
apparent way of the moon from the fun, as feen from a given place, during the
time of the eclipfe in that place: the duration of the eclipſe in that place de-
pends upon the velocity of the moon's apparent motion from the fun, and the
length of the line LP: thus, the partial eclipfe fig. 56 will be of longer duration
than that in fig. 57; becauſe the line L P is longer in the former than in the latter.
1055 The limit of folar eclipfes is a certain number of degrees minutes and fe-
conds which if the diſtance of the moon from her neareſt node exceeds the fun
will not be eclipſed; if it does not exceed, the fun will be eclipſed, in ſome part
of the earth or other. If the diſk of the earth and the ſhadow and penumbra
of the moon be projected in their proper fituation and dimenfions, at the mo-
ment of a conjunction, by § 1032, it may be found whether there will be an
eclipſe of the fun at that new moon, or not: and, if there will be one, what
is the quantity thereof. The femidiameter of the difk when it is greateſt is
62′ 11″, the femidiameter of the penumbra when largeft is 33 11"; the fum
of theſe, when both are greateſt, is 1° 35′ 22″: if the latitude of the moon, at
the time of a conjunction, exceeds that fum, the penumbra will not fall upon
any part of the diſk of the earth; fo that there can then be no eclipſe of the
fun, § 1032, fig. 40. The greatest limit of folar eclipfes is 17°32′; for that is the di-
ftance of the moon from her neareſt node, when her latitude is 1°35′ 22″: as may
be found by the method made uſe of to determine the lunar ecliptic limits,
§1019. The fum of the femidiameters of the diſk of the earth and penumbra of
the moon, when both are leaſt, is 1°25′ 7″: if at the time of any conjunction
the latitude of the moon be leſs than that fum, the penumbra or fome part of it
muſt fall upon the diſk of the earth; and there will be an eclipſe of the ſun.
The leaft limit of folar eclipfes is 15° 2; for that is the moon's diſtance from
her neareſt node, when her latitude is 1° 25′ 7″. In any conjunction when the
diſtance of the moon from her neareſt node is greater than the leaſt limit, but
leſs than the greateſt limit of folar eclipfes, the fun may be eclipfed partially,
or may quite efcape being eclipfed at all; according as the fum of the femi-
diameters of the diſk of the earth and penumbra of the moon exceeds the lati-
tude of the moon, at that conjunction, or falls fhort of it: fome writers, for
this reaſon, call the greateſt limits of both folar and lunar eclipfes poffible li-
mits; becauſe within thofe limits the luminaries may or may not be eclipfed:
the leaſt limits they call neceſſary limits, becauſe within thofe limits the lu-
minaries muſt be eclipſed.
A table
1
A.table of the femidiameters, horizontal parallaxes,
and hourly motions of the moon.
mean
horizont. horizont. | hourly
anomaly femi-dia. parallax motion
of the in the in the in the
moon. fyzygies. fyzygies. fyzygies.
mean
anomaly
of the
moon.
fign.deg. min. fec. min. fec. min. fec. fign.deg.
014 45 54 33 29 37 12
514 45 54 35 29 38 11 25
O 10 14 46 54
0 15 14 47 54
O
0 20 14 48 54
37 29 39 11 20
40 29 42 II 15
47 II 10
altitude
A TABLE
of the increaſe of the
horizontal femidiameter
of the moon
for different degrees
of altitude.
HORIZONTAL SEMIDIAM.
M. S. M. S. M. S. M. S. M. S. M. S.
14 30 15 015 30 16 0 16 30
Sec.
Sec.
O
17
O
Sec.
44 29
deg Sec.
Sec. Sec.
0 25 14 50 54
50 29
54 II
5
О
O
I
014 52 54
57 30
I I
3I
I
514 54 55
630
13 10 25
3
6
I
Ι
I 10 14 57 55
17 30
24 10 20
I 15 15
055 28 30
35 10 15
9
I
2
I 20 15
355 41 30 48 10 10
12
3
3
3
1234
1 2
122
olor
0 1 2
O
2
I
O
I
2
3
3
4
I 25 15
7 55 55 31 310
5
15
4
4
2
015 11 56
931 20 10
18
4
2 5 15 15 56
23 31
37 9 25
2
10 15 19 56
38 31
55
9 20
2 2 2
21
5
24
5
2 15 15 24 56
2 20 15 29 57
55 32
14
9 15
27
6
+56
4566
4
4
5
5
5
5
6
6
7
6
6
7
7
7
8
14 32
35 9 10
30
7
2 25 15 34 57
34 32
57 9
3
015 39 57
54 33
19
9
3
5 15 44 58
13 33 41
8
Alour
33
7
36
8
просо
8
76
9
9
8
9
9
10
9
ΙΟ
IO
II
39
8
9
ΙΟ
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I I
II
3 10 15 49 58
32 34
32 34 3
8 20
4 016 11 59
5
3 15 15 55 58 52 34 26
3 2016
3 25 16 6 59 32 35 14
4 5 16 16 60 12 35 56
4 10 16 2160 31 36 16 7 20
4 15 16 2660 49 36 35 7 15
4 2016 31 61
4 25 16 3561 20 37 10 7
016 39 61 33 37 27
8
8 15
059 12 34 50
8 10
52 35 36
7
00:00 | A
8 5
444 in
42
9
9
10
I I
12
12
45
IO
IO
I I
12
13
13
48
ΙΟ
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12
12
13
14
5 I
I I
I I
12
13
14
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8
0
54
I I
I I
13
13 14
15
25
57
I I
12
13
14
15
16
536 53 7 10
7 5
7
O
5
5 10 16 44 61
5 15 16 4662
5 16 42 61
4461
44 37 41
6
25
53 37 51
137 58
6
20
6 15
5 2016 4762 6/38 4
25 16 48 62
48/62 9/38
016 4962 11
113
138 8 II
13 14 16
14 15 16 17
14 15 16 18
14 15 17 18
15 16 17
14 15 16 17
18
78 13 14 15 16 17 18
81 13
6 10 84 13
14 15 16 17 18
14
15 16 17 18
86
5
87 13 14 15 16
17
18
6
O
90
13
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17
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63
12 13
66
I2 13
69
12
14
72
13
14
75
13
18
CHAP. 4.
413
ASTRONOMY
A table of the parallax of the moon at different degrees of altitude.
altitude.
M.
HORIZONTAL PARALLAX.
S. M. S. M. S. M.
061
S.M.
S. M.
54 55
055
deg M. S. M.
056
058
060
S. M.
S. M.
S. M.
S. M.
054 055
056 058
060
3
57
53 55 54 55 55 55 57
6 53 42 54 42 55 41
53 2054 20 55 19 57
12 52 49 53 48 54 46 56
754 656
1953 16 55
2152 17 54
15 51 10 52
1 49 54 51
38 48 30 50
746 58 48
18 46
15 52 9 53
1851 22 52
21 50 25 51
24 49 20 50
27 48 749
30 46 46 47
33 45 17 46
1746
36 43 41 44
39 41 57 42
29 45
44 43 31 45
4240 740 52 41 37 43
45 38 10 38 53 39 35 41
061
S.M. S. M. S.
0162 0'63
S. M. S. MS.
0/62 0163 O
55 61
55 62 55
40 61
40 62 39
1462 14
38 61 37
55 59 55 60
41 59 40 60
17 59 1660 1561
44 58 41 59 40 60
257 57 58 56 59 52 60 51
10 57 458 1 58 58 59 55
956 1 56 57 57 52 58 49
59 54 49 55 44 56 36 57 33
41 53 28 54 2155 14 56 8
1451 58 52 50 53 42 54 34
38 50 1951 952
55 48 32 49 21 50
546 37 47 24 48
644 35 45 20 46
42 25 43 9 43
0152 50
8 50 58
10 48 58
446 49
042
50 44 32
48 36 8 36 48 37
28 38
49 40
940 49 41
28 42
9
51 33 59 34 37 35
15 36
30 37
46 38 24 39
039 39
54 31 44 32 20 32
55 34
535
1635 51 36
26 37 2
57 29 25 29 58 30
30 31
36 32
41 33 14 33
46 34 19
60/27
60 27 0 27 30 28
029 030 030 30 31
031 30
63 24 31 24
58 25
25 26
2027
14 27 41 28
8 28 36
66 21 58 22
22 22
46 23
35 24
24 24 48 25
12 25 38
69 19 21 19 42 20
4 20 47 21 30 21 51 22
12 22 34
72 16 41 16 59 17
18 17
55 18 32 18 51 19
8 19 28
75 13 58 14 14 14 29 15
7811 13 11 26 11 3 38 12
81 8
8 27
8 36 8 459
84 5 38 545 5 51 6
87 249
2 49 2 52 2 55 3
900 O о
O
015 31 15 47
16
216 18
312 28 12 40
12
52 13 5
4
49239 32
9 42 9 51
320
6 16 6 22
3
83 II
O
о
о O
3 14 3 17
O
6
28 6 35
3 G
The
414
воок 3.
ASTRONOMY
The foregoing tables are taken from Caffini's tables aftronomiques printed at
Paris 1740. The first table fhews the femidiameter, the horizontal parallax,
and true hourly motion of the moon, for every 5th degree of her mean ano-
maly, when in fyzygy, the only time that eclipfes can happen: when the
mean anomaly of the moon, or her diſtance from her apogee, is leſs than fix
figns, or than a femicircle, it is to be fought in the firft column on the left
hand: when it is more than fix figns, it is fet down in the laft column on the
right hand. The ufe of the table will be beft fhewn by an example or two:
thus, if the mean anomaly of the moon be ofigns 5° or 11figns 25°, in either of
which cafes her diſtance from her apogee is the fame, her horizontal femidi-
ameter, when in fyzygy, is 14′ 45″, her horizontal parallax is 54′ 35″, and
her hourly motion 29′ 38″: again, if the mean anomaly of the moon be 4figns
10° or 7figns 20° her horizontal femidiameter is 16′ 21″, her horizontal paral-
lax is 60′ 31″, and her hourly motion 36′ 16″.
The use of the fecond table is to fhew how much the moon's femidiameter is
increaſed by her coming nearer to the zenith, as was mentioned § 1041; the
increaſe is fet down for every three degrees of her altitude: at the top of the
table, different apparent femidiameters of the moon when in the horizon are
fet down in minutes and feconds, the difference between any two that are
neareſt to each other being half a minute: for the fake of regularity, there is
put down 14 30", this is lefs than the leaft horizontal femidiameter of the
moon, which by the preceding table is 14′ 45″; and for the fame reafon, 17
is alſo put down, whereas the largeſt femidiameter is no more than 16′ 49″
in the firſt table: the intermediate femidiameters here fet down are 15 o":
15′ 30″: 16′ 0″: 16′ 30″. The given altitude of the moon being found in the
firſt column on the left hand, on the fame line, under each horizontal ſemi-
diameter, is fet down the reſpective increaſe to be added thereto in order to have
the moon's apparent femidiameter at that altitude: for example, fuppofe the
altitude of the moon be 63 degrees, if her horizontal femidiameter at that
time be 15′ 30″, the increaſe to be added is 14″; fo that her femidiameter is then
15′ 44″: if her horizontal femidiameter be 16′ 30″, the increaſe to be added
is 16″; fo that her femidiameter at the altitude of 63 degrees is 16′ 46″.
The uſe of the third table is to fhew the parallax of the moon at any altitude,
her horizontal parallax being given: for this purpoſe, different horizontal
parallaxes of the moon are fet down at the top of the table, where we find
indeed 54′, leſs than the leaſt ſet down in the firſt table, 54′ 33″; and 63',
larger than the greateſt in the firſt table, 62′ 11": this alfo is for the fake of
a Since the firſt of theſe tables was printed off, Dr. Halley's aſtronomical tables were publiſhed; theſe I
ſhall hereafter make uſe of, as often as I have occafion.
making
CHAP. 4.
415
ASTRONOMY
making the progreffion from greateſt to leaſt ſomething regular: the interme-
diate horizontal parallaxes of the moon namely 55: 56′: 58: 60:61:62:
are alſo fet down in the fame line. To find the parallax of the moon at any
altitude, let the altitude be taken in the firft column on the left hand, then,
on the fame line, under the given horizontal parallax, will be found the pa-
rallax for that altitude: thus, for example, if the moon's horizontal parallax
be 55, her parallax, at the altitude of 15°, is 53′ 7″; if her horizontal paral-
lax be 62′, her parallax at the ſame altitude of 15°, is 59′ 52″-
Additions to the preceding chapter.
1056 Some members of the R. Academy at Paris have endeavoured to
account for the circle of pale light feen round the moon, in a total eclipſe of
the fun, without allowing the moon to have an atmoſphere: for this purpoſe
the following experiments were tried by them: the image of the fun coming
through a ſmall hole into a dark room was received upon a circle of wood
or metal, of a diameter a good deal larger than that of the fun's image; then
the ſhadow of this opake circle was caft upon white paper, and there appeared
round it on the paper a luminous circle, fuch as that which ſurrounds the
moon: the like experiment being made with a globe of wood, and with ano-
ther of ſtone not poliſhed, the ſhadows of both theſe caſt upon paper were
furrounded with a palifh light, moſt vivid near the fhadows, and gradually
more diluted at a diſtance from them: and here they take notice that the lu-
minous ring round the ſhadow of the moon caſt upon white paper in a dark
room was ſeen by Wurzelbaur, in obferving the total eclipſe of the fun in
1706. The fame appearance was feen by holding an opake globe in the fun,
fo as to cover his whole body from the eye; for, looking at it through a glaſs
a little fmoaked, to prevent the eye from being injured by the glare of light
it would otherwiſe be expofed to, the globe appeared furrounded by a light
refembling that round the moon, in a total eclipfe of the fun: v. memoires
d'Academic Royale pour l'annee 1715. thus they folve this phenomenon in
the moon by the inflection or diffraction as they call it of the rays of light
paffing near an opake body, concerning which fee the introduction § 220. As for
the ſmall ſtreaks of light which are ſeen to flaſh from the moon and ſuppoſed
to be lightning, theſe they think may be explained by confidering fome of
the cavities on the furface of the moon as fo many concave mirrors which all
reflect the light of the fun nearly towards the fame point; that, as theſe are
continually changing their fituation with great velocity, by the moon's mo-
tion from the fun, the light which any one of them fends to our eye is ſeen
but for a moment: this folution, which does not ſeem to be a very good one,
3 G 2
will
416
воок 3.
ASTRONOMY
will ferve only to account for the flaſhes of light feen near the edges of the
moon's difk, where only we have any certainty of their having been obfer-
ved: if any fuch flaſhes ſhould be feen to come from the middle of the diſk,
we muſt look upon them as proofs of the moon having an atmoſphere.
1057 Before we conclude theſe ſpeculations about the atmoſphere of the
moon, it may not be improper to mention, that, ſome French aſtronomers
obferving through a teleſcope an occultation of venus by the moon which
happened june the 28, 1715, new ftyle, in the day-time, perceived venus to
change colour, when near the moon, for about a minute of time before fhe
was covered; they faw the like change of colour in venus immediately after
ſhe came into view again from behind the moon; at both theſe times, the
edge of the diſk of venus that was nearest to the moon appeared of a reddiſh,
the oppofite edge that was farthest from the moon of a blewiſh colour. Theſe
appearances, which feem to favour the opinion of the moon having an atmo-
ſphere, were thought to be owing to the obſervers directing the axes of
their teleſcopes towards the moon; this would neceffarily caufe any planet
or ſtar near the edge of the moon's diſk to be ſeen through thoſe parts of the
glaffes that are near their circumferences, and confequently to appear colour-
ed: for every body who has made uſe of teleſcopes knows that a lens is a
kind of circular priſm, and gives the prifmatic colours, to any objects that
are ſeen through any part of it that is diftant from its axis: and therefore a
planet which ſhines with its own light, when ſeen in the center of the aper-
ture of a teleſcope, will when at a diſtance from that center become colour-
ed, in the fame manner that venus was at the occultation just now mention-
ed: accordingly, the fame year 1715 july the 25, an occultation of jupiter by
the moon was obſerved by the fame aftronomers who had ſeen venus change
colour, and by divers others, who were particularly attentive to this circum-
ſtance, and none of them was able to perceive any change of ſhape or colour
in jupiter, whilſt they kept him in the middle of the teleſcope. Maraldi in
his memoire upon this ſubject 27 juillet 1715, fays that he had obferved, be-
fore this, two other occultations of venus, and one of jupiter, and was always
attentive to fee whether thoſe planets changed their figure or colour, either
upon the approach of the moon to cover them, or at their firſt coming again
into fight; and could never diſcover any fuch change: that, in a great num-
ber of occultations of fixt ſtars by the moon, he never could obſerve any
change, except that once a fixt ſtar increaſed a little its diſtance from the moon,
as it was going to be covered by her; but this he ſuſpected might be owing
to his teleſcope being directed fo as to have the ftar feen too far from the
middle of the apperture thereof: and concludes that all theſe obſervations
confirm,
CHAP. 5.
417
ASTRONOMY
confirm, what almoſt all aſtronomers who have made uſe of teleſcopes ac-
knowledge, that the moon has no atmoſphere. He remarks farther, that at
Montpellier, perhaps becauſe the air is clearer there than at London, the lu-
minous ring round the moon appeared much larger than it did at London;
that it was very white near the moon, and, gradually decreaſing in bright-
nefs, formed round her a circular area of about 8 degrees in diameter: if fays
he, this light was cauſed by the atmoſphere of the moon, of what a prodigi-
ous extent muſt that atmoſphere be? Dr. Pound obferving the laſt mentioned
occultation of jupiter could perceive no change of ſhape or colour in that
planet. Phil. tranſ. n. 347.
CHAP. 4. THE FREQUENCY OF ECLIPSES: THEIR RESTITUTION:
THEIR USES.
1058 For the frequency of eclipfes, take the following lemmata. 1,The moon
can fall into the earth's fhadow, only when ſhe is in oppofition. 2, The moon
can caft her ſhadow upon the earth, only when ſhe is in conjunction. 3, If the
plane of the moon's orbit were coincident with the plane of the ecliptic, fhe
would fuffer a central eclipſe every full moon; and would cauſe a central e-
clipſe of the fun, every new moon. 4, Since the plane of the moon's orbit
makes an angle of about 5° with the plane of the ecliptic, the moon may of-
ten be in oppofition, when ſhe is farther from her neareſt node than her e-
cliptic limits reach; and then ſhe will have latitude enough to eſcape being e-
clipſed by the ſhadow of the earth. 5, In like manner, the moon may often be
in conjunction, when ſhe is farther from her neareſt node than the folar ecliptic
limits reach; and then her latitude will be fo great, that her penumbra will
not fall upon the earth, and confequently will not cauſe any eclipſe of the
fun. 6, Since eclipſes can happen only in fuch conjunctions or oppofitions as
fall out when the moon is in or near one of her nodes, the fun muſt always
be in conjunction or nearly fo with one of the nodes, at the time of every e-
clipſe of the fun or moon. 7, If the orbit of the moon continued always paral-
lel to it ſelf, the line of nodes continued would always be terminated in the
fame two oppofite points of the ecliptic; and then the fun would always be
in the line of nodes at the fame times of the year: thus, if onè node of the
moon continued invariably in the point r, the other in the point ≈, the
fun would be in conjunction with the nodes exactly at the times of the two
equinoxes, and at thofe times only. 8, The times when the fun is in conjunction
with the nodes in any year are the middle of what may be called the jeaſons of
ecliples
418
BOOK 3.
ASTRONOMY
}
eclipfes for that year; for at thoſe times only, or within a few days before or
after thoſe times, can the fun or moon be eclipfed, that year. 9, The orbit of
the moon is not carried parallel to it ſelf, as was fhewn § 961 and 963; but
in ſuch a manner that the nodes have a flow motion contrary to the order of the
ſigns, ſo as to go round the ecliptic in about 19 years: this motion is at the
rate of about 19 degrees in a year, and is the cauſe that the fun comes every
year about 19 or 20 days ſooner to his conjunction with each node, and con-
ſequently, each of the ſeaſons for eclipfes comes in 19 or 20 days fooner, than
in the year immediately preceding: thus, fuppofe the moon's afcending node
& were, on the 10th of march this preſent year in the point r, her defcending
node & in the point, the middle of the firſt ſeaſon of eclipfes would this
year be on the 10th of march; the time of the middle of the next ſeaſon of
eclipſes would be about the 2d of feptember, about 10 days before the fun
gets to; becauſe the nodes will, in the intermediate time, have gone back
near 10 degrees. In the next year, & will be gone fo much back, that the
fun will be in conjunction with it in the 11th degree of , about the 18th
day of february, which will be the middle of the firſt ſeaſon of eclipſes that
year; the middle of the next ſeaſon will be about the 13th of auguft, when
the fun will be in conjunction with & near the beginning of ", &c. 10,
The mean motion of the moon from her node is 13° 13′ 46″ in a day,
fo much more than her periodical motion, given § 958, as the retrograde mo-
tion of her nodes in a day amounts to. v. Hallei tabb. The moon then paſſes
from one node to the other in 13d 14h32′ 48″: which is 1d3h 49′ 13″ lefs
than the time of a mean femilunation, wherein the moon paffes from one fy-
zygy to another: in that 1d 3h 49′ 13″ the moon's motion from her node is 14
with a few minutes and feconds. II, Hence we may fay in general, if the
diſtance of any fyzygy from the node be given, the diſtance of the two ad-
joyring fyzygies may be known; thus if a given fyzygy is in either of the
nodes the immediately preceding fyzygy and that immediately following will
be about 14° from the other node: on the other hand, if a given fyzygy is a-
bout 14° from either of the nodes, one of the adjoyning fyzygies, either that
immediately preceding or that immediately following, will be in the oppofite
node, or very near it. To apply this to eclipfes,-1, If a given new moon be in
2, there will be a central folar eclipfe, but the full moon immediately pre-
ceding, and that immediately following will efcape being eclipfed, as being
14° from 8, and confequently without the lunar limits, which are not more
than 11° 16′, § 1019.-2, If a given new moon happens when the moon is
about 14° from &, one of the adjoyning full moons must be eclipſed in
or very near it.—3, If a given full moon be in &, each of the adjoyning new
moons
CHAP. 5.
419
ASTRONOMY
moons is about 14° from 8, and therefore the fun will be twice eclipfed, be-
cauſe the folar ecliptic limits exceed 14°, § 1055: but theſe eclipſes of the fun
muſt be very ſmall, by reaſon of the great diſtance of the moon from her
node.-4, If a given full moon be about 14° from, one of the adjoyning
new moons muſt be in or near &, and cauſe a central eclipſe of the fun, or
nearly central.
4:
year, cannot be leſs
There may be 2 e-
There may be 2 of
The number of the eclipses of both luminaries, in one
than 2, nor more than 7: the moſt uſual number is
clipfes of the fun and 2 of the moon in 6 lunar months.
the fun, and fometimes, though rarely, 2 of the moon in 5 months: qui plura vult
buc spectantia, adeat Ricciol. Almag. lib. 5. cap. 14. & Tacquet Aftr. 1. 4. c. 9.
1059 Since the ecliptic limits of the fun are greater than thoſe of the moon,
general eclipfes of the fun muſt be more frequent than eclipses of the moon.
Since every eclipfe of the moon is vifible to an entire hemiſphere of the earth,
whereas, the moon's penumbra, being leſs than the diſk of the earth, can
paſs over only a part, and fometimes paffes over a very ſmall part of an he-
miſphere of the earth; eclipses of the moon will be more frequently visible in
any given place, as Cambridge, than eclipfes of the fun. Since both the fo-
lar and lunar ecliptic limits are near the moon's nodes, eclipfes can happen
only in thoſe fyzygies which fall out when the moon is in one of her nodes,
or fo near one of them as to be within the ecliptic limits: thus, an eclipſe of
the moon can happen only when ſhe is in oppofition, ſo near one of her
nodes as to be within the greateſt lunar ecliptic limit of 11° 16', § 1019: the
fun can be eclipſed only when the moon in conjunction is fo near one of her
nodes as to be within the greateſt folar ecliptic limit of 17° 32', § 1055.
1060 The reftitution of eclipfes, to the fame ſtate, as to the time of year,
quantity, duration, &c.gr. dπoxálásaris, depends upon the return of the fol-
lowing elements to the ſame ſtate;-1, The fun's geocentric place in the
ecliptic. 2, The moon's place in the zodiac. 3, The place of the moon's apo-
gee in the zodiac. 4, The place of the moon's afcending node. The motions
of the moon and the apparent motion of the fun are ſtrictly ſpeaking incom-
menfurable; and therefore the exact reftitution of all theſe elements to the
fame ſtate, is not to be expected: but they all return fo nearly to the fame
ftate in 18 years II days 7 hours 43 minutes and 20 feconds, as to produce
eclipfes remarkably correfponding, though not in all points fimilar, to thoſe
at the beginning of the period: this period which confiſts of 223 lunar months
was known to the ancients. Pliny N. H. 1. 2. c. 13. Ptolemy 1. 4. c. 2.a
‘a Ptolemy by os. Er waλalego probably means the Chaldeans.
Dr.
420
BOOK 3.
ASTRONOMY
a
Dr. Halley thought it of fo great uſe for finding the return of eclipſes, that he
many years ago, under this title, Saros ª five eclipfium periodus Chaldaica cur-
rentis feculi prima, publiſhed an half ſheet containing a ſeries of all the eclip-
ſes of both the fun and moon, many of them corrected by obſervations, for
18 years then paſt, beginning with the year 1701, and ending with 1718; to-
gether with the following elements: 1, the apparent time of the middle of
each eclipſe, 2, the anomaly of the fun, 3, the anomaly of the moon, 4, the
latitude of the moon. He fays that in this period of 223 lunations there are
18 years, 10 or 11 daysb, 7 hours, 43'1; that, if we add this time to the mid-
dle of any eclipfe obferved, we ſhall have the return of a correfponding e-
clipfe (that is the middle time of it) fo near the truth, that the error will ne-
ver amount to fo much as an hour and half: and that, by the help of fome
equations or ſmall numbers to be added or ſubſtracted, we may find the like
ſeries of eclipſes for ſeveral ſubſequent periods: He fays likewiſe, that he had
then made a table of thoſe equations to every 10 degrees of the anomalies,
but intended a more compleat one. In his tables now publiſhed, in the ſheet
Pp, we have this feries reprinted, with equations for every 5 degrees of the
fun's mean anomaly, and of the annual argument of the moon's apogee, with
the omiffion only of 5 folar eclipfes, 4 of which are very ſmall ones, and vi-
fible only near the poles. The proper uſe of it is from obfervations of the
eclipſes of any given period of 18 years paſt to know nearly the times of any
eclipſes of the ſubſequent period, which one has a mind to calculate. The
perfon who publiſhed Halley's tables fays in his preface that, as he had given
us Pound's tables of the lunar periods which are exceedingly uſeful in calcu-
lating eclipſes, he has omitted this feries, as not perfectly exact, and being
of little uſe after a few periods; however, I find it in my copy, and in ano-
ther that I have ſeen: I fuppofe, upon farther confideration, he did not think
proper to ſuppreſs any part of what ſo great an author had prepared for the
public.
1061 The uſe of eclipfes in aftronomy is this, that by two lunar eclipfes, alike
in all circumſtances, but very far diftant from each other in time, the periods
of the moon's ſeveral motions may be accurately determined. By eclipfes al-
a Whiston, from Eufebius's Chronicon, has fhewn that the Chaldean Saros was a period of 10 years, and
that therefore that name is improperly given to this of 18 years. See his New Theory, Hypoth. 10. See
allo Pearfon upon the creed, p. 65.
b 10 days if there be 5 leap years in the period, and 11 days if there be but 4 leap years therein.
c If from the fun's place in the ecliptic the mean longitude of the moon's apogee be ſubſtracted, the re-
mainder is called the annual argument of the moon's apogee: thus, if when the fun's place is in 28° of V the
moon's apogee be in the point Y, the annual argument of the moon's apogee is then faid to be 28°. The
annual argument of the moon's afcending node is found after the fame manner: fee Newton's theory of the
moon in Gregory's aftronomy book 4.
fo
СНАР. 5.
421
ASTRONOMY
alfo, eſpecially lunar ones, the epochs of the moon's mean motion are fixed;
the excentricity of her orbit, the places of her apogee and of her nodes are
found, with greater exactneſs than by any other obfervations: by obfervati-
ons of the moon made at different times it is found that ſhe is ſubject to few-
er irregularities in her motion when in fyzygy than in any other fituation:
among the fyzygies thoſe which are ecliptical are of all others fubject to the
leaft irregularity, becauſe the fun is then in or near to the line of nodes, and
gives the leaſt diſturbance to the moon's motion: in a folar eclipſe the moon's
parallax muſt be taken into the account, in order to find her place; but, the
moon being in oppofition at the middle of a lunar eclipſe, her place is then,
without confidering her parallax, deducible from the fun's place, which is
one of thoſe things that are best known in aſtronomy.
1062 The epoch called by fome the radix or root of the mean motion of
planet is fome point of mean time in a given meridian at which the mean
place of the planet in its orbit is known: according to fome writers, the e-
poch of the mean motion of a planet is fome point of its orbit wherein the
planet is, at fome known moment of mean time, in a given meridian: the
word, in greek epoche, fignifies a ftop; as time is in a continual flux, and the
motion of every one of the heavenly bodies round its orbit, is in a continual
progreffion, it is neceffary to fix upon ſome moment of time, and ſome point
in the orbit, for a beginning from whence we are to meaſure, either forward
or backward, what the mean motion of a planet is, during any known inter-
val of time, in order to find what its longitude is at any time required: thus
Newtona takes the noon of the laſt day of december A. D. 1700 at the R.
Obſervatory at Greenwich, for an epoch, at which time, he gives us (I fup-
poſe from Flamsteed's obfervations,) the mean place of the fun, or his place
according to his mean motion % 20° 43′ 40″, the mean place of his apogee
7°44′ 30″, the mean place of the moon 15° 20′ 00″, of her apogee
* 8° 20′ 00″, of her aſcending node î 27°24′ 20″: this epoch is made uſe
of in Halley's tables. How an epoch is determined by eclipſes may be ſeen
in the remarks, § 1070.
MAN
1063 The mean motion of a planet is fuch as it would have if it were mo-
ved equably in a circle round the fun: the mean motion of the moon is ſuch as
ſhe would have if ſhe moved equably in a circle round the earth: `this equa-
ble motion is fuppofed, in order to facilitate the calculations which are made
to find their places, at any given time; for, the mean place of a planet being
found at any time, aftronomers teach how to find its true place for that time;
in a ſhort way of expreffing themſelves, they frequently call the place where-
a princip. Schol. l. 3. prop. 35-
3 H
in
422
BOOK 3.
ASTRONOMY
in a planet would be found if its motion were mean or equable, its mean
motion: thus, in Halley's tables, by the epochs of the mean motion of the
fun and moon, of their apogees &c, is meant the places where theſe would
be at the times there mentioned, if their motion were equable: that the fun
is in one of the focuſes of the elliptic orbit of every planet, and that a line
drawn from the fun to the periphery of the orbit deſcribes equal areas in e-
qual times, has been before mentioned, § 669, 671: if the other focus where-
in the fun is not be confidered as the center of a planets motion, a line drawn
from that focus to the planet will defcribe nearly equal angles in equal times;
for which reaſon, ſome aftronomers call that point the center of the planet's
mean or equable motion: fee this fubject largely treated of by Keill, in his 22,
and 24 aftronomical lectures.
23
1064 The uſe of epochs is beſt ſeen by an example: let it be required to find
the mean place of the moon for any given moment of time; find in the ta-
bles what the mean motion of the moon is during the interval of time
between the moment given and the epoch, and if the moment given be
after the epoch, add that mean motion to the moon's place at the time of
the epoch; if the moment given preceeds the epoch, ſubtract the mean mo-
tion from the moon's place at the time of the epoch, and you will have the
mean place of the moon at the time required: thus, if I would have the
moon's mean place january the 20th 1749 at 12h; the interval between that
time and the epoch dec. 31, 1700 is 48 years 20 days 12h, during which, by
Halley's tables, the moon's mean motion is 5° 8° 40′ 46″; that is, caſting away
all entire revolutions in her orbit, the moon's mean place during that inter-
val, is ſo much advanced forward according to the order of the figns from
≈ 15° 20′, her mean place at the epoch: add 5º 8° 40′ 46″ to ≈ 15° 20′, and
the moon's mean place 1749 jan. 20th 12h, comes out 24° 0′ 46″.
Scholium. If the mean place of a planet at a given time in a given meridi-
an be found, it is eaſy to find its mean place for a given time in any other
meridian, the difference in longitude between thoſe two meridians being
known: fee § 333.
1065
The ufe of eclipfes in geography, is to diſcover the different longitude
of different places, for which lunar eclipſes are moſt uſeful: this way howe-
ver is liable to ſome ſmall inaccuracy, even with teleſcopes, becauſe of the
difficulty of diſtinguiſhing with them exactly the ſhadow of the earth from
the penumbra: fee § 998. Flamsteed in his doctrine of the ſphere pag. 60. &
Caffini, Hift. d'Acad. ann. 1707, teach how the longitude may be found by
obferving the beginning or end of a folar eclipfe, but this requires the know-
ledge of the moon's parallax, and ſome computation befides: fee Keill's 14th
aftronomical lecture.
1066
СНАР. 5.
423
ASTRONOMY
1066 The uſe of eclipfes in chronology, is to determin exactly the time of any FIG.
paſt event: for there are ſo many particulars obfervable in every eclipſe, as the
time of the day, the place where vifible, the quantity of the eclipfe, &c, that
it is hardly poffible two eclipſes ſhould happen within the compaſs of
years exactly alike in all circumſtances: if therefore any paſt eclipſe be record-
ed in hiſtory, with ſome of thoſe circumftances, it may be computed how long
ago it happened, by tables of the motions of the fun and moon.
remarks.
Remarks upon § 1062.
many
See the
1067 To find the moon's true place by a lunar eclipfe: find the moment of
the middle of a lunar eclipſe, by obſerving the beginning and end thereof; or
two times when the eclipſe is of the fame quantity, one a little after the be-
ginning, the other a little before the end of the eclipſe: calculate for that mo-
ment the fun's place, oppofite to which is the place of the center of the earth's
ſhadow; as is alſo the place of the moon, if the eclipſe be central: if the e-
clipſe be not central, take the diſtance of the center of the ſhadow from the
node, which is meaſured by the arc of the ecliptic E C, fig. 58, now in the 58
ſpherical triangle ECA rightangled at A, the hypotenuse EC being known,
and the angle CE A given 5° 17,§ 1019; the arc AE the diſtance of the moon
from her node meaſured in her orbit may be found. Draw A B, in the trian-
gle A B E rightangled at B, the hypotenuſe A E and the angle A E B are known;
from whence, the arc AB the moon's latitude, and the arc E B the diſtance of
the moon from her node reduced to the ecliptic may be found: this arc E B
muſt be ſubtracted from the true place of the moon's node, when it is farther
advanced according to the order of the figns than the center of the fhadow,
and muſt be added thereto, when it is lefs advanced than the center of the
ſhadow, and we ſhall have the true place of the moon reduced to the ecliptic.
1068 To find the mean motion of the moon: the true places of the moon be-
ing determined at two different moments, § 1067, we have the
apparent moti-
on of the moon during the interval between thoſe moments: this apparent mo-
tion of the moon is mean or equable, when the moon is in the fame fituation
with regard to her apogee or perigee at both thoſe moments. In order to deter-
mine the mean motion of the moon accurately, two eclipfes of the moon ve-
ry diſtant from one another in time are to be compared together; that fo the
different inequalities of the moon's motion and the errors of obſervation be-
ing divided among a great number of her revolutions, may produce the lefs
error in the determination of the moon's mean motion.
Thus Caffini F. takes the eclipfe of the moon mentioned by Ptolemy 1. 4.
3 H 2
c. 6.
424
воок 3.
ASTRONOMY
S
c. 6. to have been obſerved by the Chaldeans at Babylon, 720 years before the
birth of our Saviour; the middle of this eclipfe, reducing the time to the me-
ridian of Paris, was at 6h 48′, march the 19th N. S. calculating the fun's place,
he finds thereby the moon's place to be 5s 21° 27: he compares this with a
lunar eclipſe obſerved at Paris ſept. 20th 1717, the middle whereof was at 6h
2′, when the moon's place, being oppofite to the fun, was 11s 27° 34'. The
interval of time between theſe two eclipfes is 2437 years and 174 days, want-
ing 46 minutes; of theſe years 609 are biffextile, the number of days is then
890288 wanting 46 minutes; during which interval the moon had made a
certain number of revolutions, and was advanced befides in her orbit 6º 6° 7.
In fo long an interval of time, wherein the moon goes round in her orbit
above 30000 times, a miſtake of one revolution might eafily be made; for
each revolution is compleated in less than 40000 minutes; fo that reckoning
one revolution too much or too little would cauſe an error of only one mi-
nute and a few feconds in the time of an entire revolution of the moon round
the zodiac. In order to avoid fuch miſtake, the abovementioned author exa-
mined fome pairs of eclipfes that had a much ſhorter interval between, ſo ſhort
that the number of the moon's revolutions during the fame may be known
with certainty: thus, he confidered an eclipfe of the moon the middle where-
of happened the 9th of feptember 1718 at 8h 4, when the fun's true place
was 5s 16° 40′, with another eclipfe the middle whereof was obſerved at 8h
32′ auguft the 29th 1719, when the place of the fun was 5º 5° 47. There
are in this interval 354 days and 18 minutes, during which the moon made
13 revolutions wanting 10° 53': this is at the rate of 27d 7h 6′ each revolu-
tion of the moon round the zodiac: this laſt number of days &c was made
ufe of to compare eclipfes at a greater diftance from each other.
Thus, comparing an eclipſe of march the 15th 1699 at 7h 23′ at night, when
the fun's place was 11s 25° 30 with one of march the 27th 1717 at 3h 16′ in
the morning, when the fun's place was os 6° 21′, he finds the interval be-
tween is 18 years, 4 of which are biffextile, and 11d 7h 53′; wherein the
moon, beſides a certain number of entire revolutions, is advanced 10° 51′ : if
we reduce this interval which contains 6585d 7h 53′ into minutes, and di-
vide thofe minutes by the number of minutes contained in 27d 7h 6′, the time
of one revolution of the moon, the quotient will be 241 with a fraction of
about; which fhews that during the interval the moon had
4
gone through
241
revolutions, or 241 times 360°, and an arc of her orbit of 10° 51′: re-
duce thoſe 241 revolutions with the arc of 10° 51′ into minutes of a degree,
and then ſay, by the golden rule, as the number of minutes of a degree in the
moon's way during the interval, to the number of feconds of time in the in-
terval
CHAP. 5.
425
ASTRONOMY
terval, ſo is the number of minutes in 360° to a fourth number, namely the
feconds of time wherein the moon makes one revolution round the zodiac;
this will bring out 27d 7h 43′ 6″, which gives us more exactly the mean re-
volution of the moon; and this we may make uſe of in comparing eclipſes
with greater intervals between them, in order to arrive at ftill greater exact-
nefs.
It has been already ſaid that between the eclipſe on the 19th of march 720
years before Chriſt and that on the 20th of feptember A. D. 1717 there was
an interval of 890288 days wanting 46 minutes; if this be divided by 27d7b
43′ 6″, there will come out 32585 revolutions and a little above half a revo-
lution, which half anfwers to 6s 6° 12, the difference between the places of
the fun at the middle of theſe two eclipfes: if therefore we fay as the mi-
nutes in 32585 revolutions with 6s 6° 12′ to the feconds in 890288 days want-
ing 46 minutes, fo are the minutes in 360° to a fourth number, this will
bring out the mean revolution of the moon 27d 7h 43′ 5″; which is the moſt
exact that can be had, being deduced from 2 eclipſes very far diftant in time
from each other: and differs but one fecond from what was computed be-
fore. The fame quantity is brought out by Caffini, from the interval between
an eclipſe of march the 19th in the year 199 before Chriſt and that before
mentioned upon the 19th of march 720 years before Chriſt, as alfo from the
interval between the eclipſe of the year 199 before Chriſt and that of feptem-
ber the 20th A. D. 1717.
1069 The time of a mean revolution of the moon being thus known, the
mean motion of the moon in a day or an hour or a minute is eaſily found,
by the golden rule: thus, as 27d 7h 43′ 5″ to 360°, fo is 1 day to 13° 10′ 35″
the mean daily motion of the moon: if 13° 10′ 35″ be divided by 24,the mean hourly
motion of the moon will appear to be 32′ 56″ 27″: if 32′ 56″ 27″ be divided
by 60, we ſhall have the moon's mean motion for a minute 32" 57". Again, if
we multiply the moon's daily motion 13° 10′ 35″ by 365, the number of
days in a common year, we ſhall have the moon's mean motion in a common
year: in like manner, may the mean motion of the moon be found for hun-
dreds or thouſands of years, in order to conftruct tables of the moon's mean
motion. So Caffini; but by this way fmall errors multiplied may become
confiderable: it is better to uſe the method prefcribed in the foregoing fecti-
on, and fay as the interval of time between two eclipfes at a great diſtance
from each other to the moon's mean motion during that interval; fo is any
other interval of 50, 100, or 1000 years to her mean motion during thoſe
years.
1070 It has before been faid that the moon does not move equably in her
orbit,
426
BOOK 3.
ASTRONOMY
FIG. orbit, but is fwifteft in perigee, floweft in apogee with a mean motion at her
mean diſtances; this difference in the moon's motion is called by fome aftro-
nomers her firſt inequality. To determine an epoch of the moon's mean motion,
the place of her apogee, and her firſt inequality: for this purpoſe, a great number
of lunar eclipfes are to be compared together in the following manner; take
the interval of mean time between two eclipfes, which according to the
order of time may be called the first and fecond, and find in the table of the
moon's mean motion the number of figns degrees minutes and feconds which
anſwer to that interval: add theſe to the moon's true place in the firſt of theſe
eclipfes, or fubtract them from the moon's place in the ſecond eclipſe, and
note how much the moon's place at each eclipfe, by thus calculating it, comes
out different from her true place found by the fun's place: repeat the opera-
tion with a good number of other eclipfes, comparing them with the firſt e-
clipfe, and mark thoſe where the difference between the moon's true place
and her place thus calculated is greateſt both in exceſs and in defect; if the
greateſt defect and greateſt exceſs be equal, it is a proof that the moon at the
time of the first eclipfe was in her perigee or apogee, and that her mean place
was then the fame with her true place: in which cafe, each of theſe differen-
ces is the greateſt equation of the moon in fyzygy, that is the greateſt quantity
that is ever to be added to or fubtracted from her mean place in order to de-
termine her true place in fyzygy: if the greateſt defect and exceſs be not e-
qual, half the fum of them will meaſure the greateſt equation of the moon:
and if from the greateſt equation of the moon we fubtract the leaſt of the
differences, we ſhall have the equation of the moon at the time of the firft
eclipfe; and this being added to or fubtracted from the true place of the
moon will give the mean place of the moon at that time.
59
To determine the place of the moon's apogee: in fig. 59 let ABP be the or-
bit of the moon, A her apogee, P her perigee, c the center of her elliptic
orbit, T the place of the earth, F the other focus, or center of the moon's
mean motion: we may, by means of the greateſt equation TBF, find out the
moon's excentricity; that is, what ratio CT has to AC the femiaxis of the el-
lipfis ABP: this being found, draw out TR to M, making Tм equal to AP;
joyn FM, and fay as TF to TM or AP, fo is the fine of the angle TMF which
by Eucl. 1. 5 & 32 is the half of F RT the equation of the moon at the time
of the firſt eclipſe to the fine of the angle TFM or AFM: from AFM thus
found ſubtract TMF, the remainder ATR meaſures the moon's diſtance from
her apogee at the time of the firſt eclipſe.
Example. Let the firſt eclipſe be a total lunar one the middle whereof was
dec. 10, 1685 at 10h 38′ 10″ mean time at Paris, when the moon's place was
in
CHAP. 5.
427
ASTRONOMY
in 19° 40′ 0″ of II: this was compared with other ſubſequent eclipfes, where- FIG.
of thoſe only are here related wherein the greateſt difference was found be-
tween the true and mean place of the moon. Between the years 1685 and
1720 there was a total eclipfe on the 16th of may 1696, the middle whereof
was at 12h56″ mean time at Paris, between this and the firſt eclipſe dec.
10th 1685 there was an interval of 10 years, 3 of them biffextile, 157d լի
29′ 46″, in which time the mean motion of the moon is 5º 12° 53′ 10", this
added to 2º 19° 40′ o" the true place of the moon at the firſt eclipſe gives her
place 8° 2° 33′ 10": whereas the moon's true place at the ſecond eclipſe was
7$ 26° 53′ 35″, the difference between theſe two places is 5° 39′ 35″. The
next eclipſe compared was of the year 1699 march the 15th the middle where-
of was at 7h 14′ mean time at Paris: between this and the firſt eclipſe of
dec. 10th 1685 the interval was 13 years 94d 20h 35′ 50″, the mean motion
that anſwers to this is 3º 1° 24′ 47″, which added to the true place of the moon
at the firſt eclipſe of dec. 10th 1685 gives 5º 21° 4′ 57″, now the moon's true
place at the middle of the eclipſe of march the 15th 1699 was 5º 25° 28′ 41″
which exceeds the place calculated 4° 23′ 54″; whereas the true place of the
moon in the eclipſe of 1696 falls ſhort of the place calculated 5° 39′ 35″. As
in all the eclipſes between the years 1685 and 1720 thoſe of 1696 and 1699
fhew the greateſt difference in exceſs and defect between the calculated and the
true place of the moon, thoſe differences are to be added together, the ſum
whereof is 10° 3′ 29″, the half of this 5° 1′ 44″ is the moon's greateſt equa-
tion. If from 5° 1′ 44″ we take the leſs difference 4° 23′ 54″ we ſhall have
the firft equation of the moon at the eclipfe of 1685, 0° 37′ 50″, this being
taken from 2s 19° 40′ 0″ the true place of the moon at that time, we ſhall
have the mean place, dec. 10th 1685 at 10h 38′ 10″, 2° 19° 2′ 10″; which
may be taken for an epoch of the mean motion of the moon. The greateſt
equation of the moon being determined 5° 1′ 44″, in fig. 59 the angle TBC 59
will be 2° 30′52″, fay then, as the whole fine is to the fine of the angle TBC
of 2° 30′ 52″, ſo is TB or AC 100000 to c T ; which comes out 4387, for the
moon's excentricity: thus, we find that, if the mean diſtance of the moon
from the earth were divided into 100000 equal parts, the excentricity of the
moon would be 4387 of thofe parts. Again, fay as TF which is 8774 is to
TM or AP, which is 200000; fo is the fine of TMF or o° 18′ 55″, half the
moon's equation at the time of the eclipſe of 1685, to the fine of TFM of
AFM; which angle will be found 7° 12′24″: take from this TMF of 18′ 55″
there remains ATR of 6° 53′ 29″, the diſtance of the moon from her apogee
at that time: add this to the true place of the moon, which was then in 19°
40′ o" of I, and we have the place of her apogee, on the 10th of december
1685, at 10h 38′ 10″ in the evening, in 26° 33′ 29″ of 1.
In
428
BOOK 3.
ASTRONOMY
In the conclufions drawn from all thefe operations it is fuppofed that, in
the fyzygies the equations of the moon are equal at equal diftances from her
apogee on either fide thereof, and that, in fo great a number of obſervations
as have for this purpoſe been made ufe of, fome of them have happened to
be made at a time when the moon was at her mean diſtances, when the equa-
tion is greateſt of all; and no other inequalities of the moon have been here
confidered but ſuch as are owing to the excentricity of her orbit, and the in-
equality of motion arifing from that excentricity, whereof mention was made
$ 952. We fhall hereafter ſee that the moon has fome other ſmall inequalities
which are cauſed by the different diſtances of the ſyſtem of the moon and
earth from the fun.
1071 The foregoing example is fufficient to fhew the method of finding
the mean place of the moon, and the place of her apogee, in order to ſettle
an epoch of them; as alſo to determin the firſt inequality, or the greateſt e-
quation of the moon in fyzygy: but, as all obfervations made ufe of for this
purpoſe are liable to ſmall errors, the way to come at the greateft exactneſs
poffible in this and many other cafes in aftronomy is to compare a great num-
ber of obfervations together, and take the mean which refults from them all,
as nearest to the truth: this Caffini tells us he has done with regard to the
fubject before us, and from fuch compariſon he concludes that, on the 10th
of dec. 1685 at 10h 38′ 10″ in the evening, the mean longitude of the moon
was 2° 19° 8′ 55″, the place of her apogee 2s 24° 32, and her greateſt equa-
tion in fyzygy 4° 58′ 44″: which numbers are a little different from thoſe
mentioned in the example.
1072 To find the motion of the moon's apogee: if the place of the moon's a-
pogee at the times of different eclipfes diftant fome years from each other be
found, by the method taught in the foregoing fection, it will appear not to
be fixt, but to be at different times in different parts of the zodiac. The
place of the moon's apogee on the 10th of december 1685 at 10h 38′ was
fettled in 24° 32′ of 1, § 1071: in the eclipfe of the moon obferved at Pa-
ris
may the 16th 1696 at 12h 12, the true place of the moon was 26° 53′ 35″
of m, if we fuppofe the place of the apogee to be fixt in 24° 32′ of I, the
moon's true anomaly at that time will come out 5° 2° 21′ 35″, which would
bring out the equation of the moon's orbit but 2° 14′ 39″, whereas it
appears
by the calculations in § 1070, that it was about 5°: fo that, ſuppoſing the a-
pogee fixt, the equation which anſwered to the moon's anomaly does not give
her true place; an evident proof that the apogee had changed its fituation.
In the orbit of the moon (the fame may be faid of the orbit of every pla-
net) whatever the equation is in any one point, there are three other points
which
page 429.
Book III.
a
S
R
1
60
B
M
K
D
H
M-
A.
61
N
E-
62
B.
k
82
CHAP. 5.
429
ASTRONOMY
which have an equation equal to it: but then in two of theſe 4 points, which FIG.
are taken on different fides of the mean diſtance, and in that part of the or-
bit wherein the moon paffes from apogee to perigee, the equation is fub-
tractive: that is muſt be ſubtracted from the mean place of the moon in or-
der to find her true place: in the other two points which are taken on diffe-
rent fides of the mean diftance, in that part of her orbit wherein the moon
goes from perigee to apogee, the equations are additive: that is muſt be added
to the mean place of the moon in order to find her true place.
In fig. 60, let the outward circle repreſent the apparent orbit of the moon 60
in the ſphere of the heaven deſcribed §950, ABCD &c the orbit of the moon,
wherein ſhe is carried round according to the order of the letters, let T be the
earth, p the center of the moon's mean motion, A the moon's apogee, & her
perigee, D and K the places of her mean diſtance: when the moon is at a
her true and mean place are the fame, namely at a; for P A and T A are co-
incident, and terminate in a: at A alſo the motion of the moon is the flow-
eſt that ever it is, and confequently her true motion is then moſt of all ex-
ceeded in velocity by her mean motion: as fhe goes from A towards G her
true motion is continually accelerated, but does not become equal to her mean
motion till ſhe arrives at D, her mean diſtance: now, whilſt her true motion
continues flower than her mean, the true place of the moon muſt be conti-
nually more and more behind her mean place; becauſe, though the exceſs of
her mean motion above the true is growing gradually leſs and lefs, yet it is
ftill excefs, and the continual addition of that diminiſhing exceſs increaſes
every moment the diſtance of the mean place from the true: at D therefore
will that distance be greateſt, and the greateſt ſubtractive equation will be
there, that is, the mean place of the moon will there be fartheft advanced be-
fore the true place; and therefore the greatest arc RS muſt be ſubtracted from
the mean place R, in order to determin the true place. As the moon goes
on from D to G, her true motion begins to exceed her mean motion, and, be-
ing continually accelerated, the exceſs of the true motion above the mean
continually increaſes, and, confequently, the true place of the moon advan-
ces nearer every moment to her mean place, and the equation grows gradu-
ally lefs and lefs, till ſhe arrives at G, where the equation vaniſhes, and the
true and mean place are the fame; namely at g: for the lines drawn from T
to G or from P to G are coincident, and both of them terminate in g.
the moon is carried with her greateſt velocity, and therefore her true moti-
on there moſt of all exceeds her mean: as he goes from G to her mean di-
ſtance at K, her true motion is continually retarded, but is notwithſtanding all
the while quicker than her mean, and confequently her true place is conti-
nually
3 I
At G
430
BOOK 3.
ASTRONOMY
FIG. nually advancing farther before her mean place: fo that at к the true place
of the moon will be fartheft of all advanced before her mean place, and the
greateſt additive equation will be there; that is, there the greatest arc ik muft
be added to the moon's mean place at i, in order to find her true place at k.
As the moon goes from к towards A, the excefs of the true above the mean
motion continues, but grows continually leſs and leſs, ſo that the equation
gradually diminiſhes, till the moon arrives at A, where the equation vaniſhes,
and the true and mean place are again the fame.
60
In the figure before us, whatever the equation be at any given point in
the orbit of the moon as at c, the other three points, which are in the circum-
ference of the ellipfis at the fame diſtance from the points of mean diſtance,
as E, I, and I have the fame equation in quantity; but in c and E the equa-
tion is ſubtractive, in 1 and L additive: the fame may be ſaid of any other
four points equidiſtant from the points of mean diſtance, as B, F, H, M.
I
Immediately before the eclipfe of 1685 when the place of the moon's apo-
gee was found to be in 24° 32′ of ¤, § 1071, there was a lunar eclipfe de-
cember the 21st 1684: by comparing the interval between theſe two eclipſes
with the mean motion of the moon during the time of it, the moon's equa-
tion at the latter of them comes out 3° 44 1", fo much the moon's mean place
was advanced before her true place, which fhews ſhe was then going from
apogee towards perigee. As there are two points in that half of her orbit to
which this equation of 3° 44′ 1″ correfponds, 1s 20° 54′, and 4° 13° 44′, if we
ſubtract the firſt of theſe 1$ 20° 54′ from the moon's mean place dec. 21,1684
at 10h 55′ 58″, determined to be 3° 4° 52′ 1″, the place of her apogee comes
out 1° 13° 58′; the difference between this and the place of the moon's apo-
gee dec. 10th 1685 is 1s 10° 34; this meaſures the motion of the apogee in
the ſpace of 354 days wanting 17 44", which gives the daily motion there-
of 6′ 52", and the entire revolution of it 8 years and almoſt 9 months: if we
fubtract the ſecond place of 4° 13° 44′ from the moon's place dec. 21ft 1684,
as before determined, it will bring out the time of an entire revolution of the
moon's apogee about 3 years, very different from the former determination.
As theſe two obfervations alone are not fufficient to determin which of the
two periods 3 years or 8 years and almoſt 9 months is neareſt the truth, it is
neceffary to compare them with other obfervations made nearly within the
fame interval of time: accordingly, another eclipfe of nov. 29th 1686 was
compared with that dec. roth 1685, in the fame manner as the eclipfe of 1684
was, and the motion of the apogee found by one of the two points to which
the equation correfponds comes out near that of 8 years and almoſt 9 months;
whereas the other point to which the equation correfponds brings out the
motion
CHAP. 5.
431
ASTRONOMY
motion of the apogee different from both the periods before determined: thus, FIG.
the period of eight years and almoſt nine months is found to be nearly the
time of the revolution of the moon's apogee round the zodiac, according to
the order of the figns.
The motion of the apogee being thus found out near the truth, in order
to determin it more exactly, it was neceffary to compare eclipſes at a greater
diſtance in time from one another; accordingly, by comparing the places of
the moon's apogee at the eclipſe of jan. 20th 1647, and at a great number of
other eclipſes accurately obſerved with the place thereof at the eclipſe of dec.
10th 1685, Caffini determined the time of an entire revolution of the moon's
apogee to be 8 common years 311 days and 8 hours: the annual motion of
it to be 1s 10° 39′ 52″: and its daily motion 6′ 44″ 1″.
1073 The places of the moon's nodes are best determined by lunar eclipfes: if
an eclipfe of the moon be central, the moon is in one of her nodes at the
middle of the eclipſe; and the place of that node is diametrically oppofite to
the fun's place: as the circle of the earth's ſhadow is confiderably larger than
the diſk of the moon, we cannot fee two oppofite parts of the circumference
of that circle at a time, fo as to determine the place of the center thereof, and
obferve whether the center of the moon paffes under it or not; or how near
it paſſes thereto: but we may find whether an eclipſe of the moon be central
or not, by the following method: obferve the paffage of any two ſpots equi-
diſtant from the center of the moon on oppofite fides of her diſk, and fo fitu-
ated that a line drawn through them is nearly perpendicular to the way of
the moon M N, as the ſpots A and B, fig. 61, if both theſe ſpots enter into the 61
ſhadow together, and go out of it together, the eclipfe is central; other-
wife not.
The place of the neareſt node may be alſo determined by a partial eclipſe of
the moon, if at the time of the obſervation the femidiameters of the moon and
of the earth's fhadow be known in minutes of a degree: for the quantity of
the eclipſe meaſured by the line AB, fig. 62, being known by obfervation, 62
take that line from the femidiameter of the ſhadow AD, and we ſhall have
DB the diſtance of the center of the fhadow from the edge of the moon;
add to this the femidiameter of the moon CB, and we have CD the moon's
latitude: now in the triangle DCE right angled at c we have one fide có
known, and the acute angle DEC is given, being 5° 17 § 1019; from which
data ED the diſtance of the center of the earth's fhadow from the node may
be found. It is eaſy to know which node the moon is in when the eclipfe is
central, or to which ſhe is near in a partial eclipfe, by obferving fome time
before or after whether ſhe is in north or fouth latitude.
3 I 2
1074
432
BOOK 3.
ASTRONOMY
1074 To find the motion of the moon's nodes: that in every eclipſe the moon
is in or near one of her nodes, has been fhewn already, § 994, that eclipfes
fall out when the fun is in different parts of the ecliptic, that is at different
times of the year, is matter of common obſervation; from hence it appears
that the nodes have a motion in the ecliptic: in order to determine what this
motion is, the obfervations of eclipfes made in different years and at different
times of the year muſt be examined, and the places of the moon's nodes at each
eclipſe muſt be found, by the method made ufe of § 1073. Thus, by a central
eclipſe of the moon obferved at Paris april the 16th 1707, the place of her a-
ſcending node was determined to be then os 26° 19. By a partial eclipſe of
the moon march the 26th 1717 at 15h 16′ at Paris, the place of her aſcend-
ing node was then found to be at 6s 13° 29. By an eclipſe almoſt central
fept. 9 1718 at 8h 4′ the place of the aſcending node was at that time found
to be at 5º 16° 40'. By the two laſt of theſe eclipſes the motion of the moon's
nodes appears to be contrary to the order of the figns; fince the afcending
node was forwarder on the 26th of march 1717 than on the 9th of feptember
1718: the interval between theſe two obſervations is 531d oh 16′ 48″, during
which the motion of the nodes was 26° 49′ o": according to this proportion,
the motion of a node for one day comes out 3′ 2″. Again, if we compare
the eclipfe of april the 16th 1707 with that of ſeptember the 9th 1718, the
interval between is eleven years three of them biffextile 145d 18h 16, in all
4163d 18h 16, during this time the motion of the afcending node was con-
trary to the order of the figns 219° 39′; according to which proportion there
comes out 3′ 10″ for the daily motion of the node. We may find the annual
motion of the node by the golden rule, if we fay, as 4163d 18h 16′ to 219° 39′,
fo is 365d to 19° 15′ 0″, the annual motion of the node: again, if we ſay, as
219° 39′ are to 360°, ſo are 4163d 18h 16′ to 6824d7h 33'; or 18 common
years 254d7h, the time of the revolution of a node round the ecliptic. By com-
paring the interval between the eclipſe of april the 16th 1707 and another
of march the 26th 1736 with the place of the node at each of thoſe times,
the daily motion of the node is brought out 3′ 10″ 36″".
In theſe examples, eclipfes are compared together with fhort intervals be-
tween, in order to find which way the motion of the nodes is, and to deter-
mine nearly the time a node takes in going round the ecliptic; that, in com-
paring eclipſes with long intervals between, we might be ſure not to miſreckon
one or more entire revolutions of the node. There are three ancient eclipfes
recorded by Ptolemy to have been obferved at Babylon, the firſt of theſe fell
out 720, the other two 719 years before the birth of Chrift; if theſe be com-
pared with the eclipfe of feptember the 9th 1718, the interval between is a-
bove
page 433.
H
d
63
E
P
b
Book III.
H
N
64
83
F
R
e
E
P
B
a
N
65
the
S
N
66
RH
石
​P
E
d D
F
69
R
OF
S
CHAP. 5
433
A ST.RONOMY
bove 2437 years, during this time the node, befides entire revolutions, was
fo far advanced in its retrograde motion as to fhew that it moves at the rate
of 3′ 10″ 38″ in a day; which is very little different from what was before
determined from the obſervations made of eclipfes with much ſhorter inter-
vals between.
Theſe remarks beginning at § 1067 are chiefly taken from the third book
of Caffini's Elements d'aftronomie chap. 5 & feq.
1075 Scholium. When we determine the mean motion of the moon, the
motion of her apogee and nodes by comparing her place at ſome eclipſe late-
ly obferved with her place at the time of fome very ancient eclipfe, together
with the interval between, we proceed upon a fuppofition that theſe motions
are the fame now that they have always been. Halley, by comparing the an-
cient eclipſes obſerved at Babylon with thoſe obſerved by Albatennius in the
ninth century, and ſome of his own time, diſcovered the moon's mean moti-
on from the fun compared with the diurnal motion of the earth to be a lit-
tle ſwifter now than heretoforea: and fays he ſhould have been able to find
in what proportion the moon's motion has been accelerated, if he had the lon-
gitudes of Bagdat, Alexandria, and Aleppo well aſcertained: becauſe in or
near thoſe places all the obfervations were made by which the middle moti-
ons of the fun and moon are determined b.
Nicolaus Struyck author of a treatiſe of geography and aftronomy in low
Dutch oppoſes Halley's opinion of the acceleration of the moon's motion;
but the ſhifts he makes ufe of to evade the force of the proofs arifing from
the difference between the obſerved and the computed places in the ancient
eclipſes are very extraordinary: for, three eclipfes which Ptolemy in expreſs
words of Hipparchus relates to have been brought from Babylon as obſerved
there, he pretends muſt have been obferved at Athens; for no better reaſon
than this, that Hipparchus, in ſetting down the times of them, fays who was
the chief magiſtrate at Athens the year of each eclipfe; and mentions the
Attic month wherein it happened: whereas, this was as natural for Hippar-
chus who wrote in greek to do, as it would be for a Roman hiſtorian writing.
in latin to diſtinguiſh the time of any event which fell out in a diſtant coun-
try by faying who were confuls at Rome that year. Again, three other eclip-
ſes faid expreffly by Hipparchus to have been obſerved at Alexandria this au-
thor would have us believe were obſerved at Athens, becauſe the times of them.
a Newt, princip. edit. Cantab. 1. 3. prope finem.
b Phil. tranfact. n. 218.
་
Ο ταυλαι μεν δη Τρεις εκλέψεις παραλέθειςθαι φησιν [ Ιππαρχο ] απο των εκ Βαβυλον θα διακομισθέντων, ως
Exes Telngnuevas. Ptolem. μɛyaλ. ounlaž. p. 105. edit. Bafil.
d ας φησιν [ Ιππαρχο] εν Αλεξανδρεια τεληρησθαι. Ptolem. ibid. p. 106.
1
are
434
воок 3.
ASTRONOMY
FIG. are marked by the years of the Calippic period, which was the invention of
a Greek and made ufe of by the Greeks. Now I think no body could have
reaſoned in this manner againſt a plain affertion of matter of fact who had
confidered that Hipparchus makes uſe of the Calippic period in the fame man-
ner, in fetting down the times of feveral equinoxes obſerved by himſelf at
Alexandriaa, as he does alſo in other obfervations, and that Timocharis who
obſerved at Alexandria long before him did the fame c.
Since the above mentioned declaration of Halley the longitude of Alexan-
dria has been determined by Chazelles, from which that of Babylon may al-
fo be known, that place being according to Ptolemy 50 minutes in time eaſt
from Alexandria: having theſe data Mr. Dunthorned compared feveral anci-
ent and modern eclipſes with the calculations of them by his own tables, and
found the truth of Halley's opinion confirmed. In one of theſe eclipſes obſer-
ved at Babylon in the year before Chrift 383, dec. 22. the moon is faid to have
begun to be eclipſed half an hour before the end of the night, that is half an
hour before fun-riſe, and to have ſet eclipſed, whereas by the tables the ſetting
of the moon in that place comes out above an hour before the beginning of the
eclipſe; this fhews that the moon's place was at that time 40 or 50 minutes
of a degree forwarder in her orbit according to the order of the figns than the
tables repreſent her: fo that, in going from her place wherein ſhe was at the
time of this eclipfe to her place wherein fhe was, for example, at the epoch
mentioned § 1062, the moon has gone 40 or 50 lefs way, than by the ta-
63 bles: let fig. 63 repreſent the orbit of the moon wherein the moves accord-
ing to the order of the letters, let a be the place of the moon at the epoch, c
her true place at the time of the ancient eclipſe as obſerved, b her place at
that time by the tables; it is manifeft that from the time of the ancient eclipſe
to the epoch the moon's true motion has been only the arc cdea, whereas the
tables make her motion to have been a greater arc bcdea: the moon there-
fore during the interval of time between the eclipſe and the epoch has had
leſs motion, that is, her motion has been flower than the tables give it.
In another eclipſe obſerved at Alexandria in the year before Chriſt 201,
ſept. 22. Hipparchus fays the moon began to be eclipſed half an hour before
her riſing, whereas the tables make the beginning of the eclipſe about 10 mi-
nutes after the rifing of the moon in that place, that is about 40′ later than
the beginning by obfervation, ſo that the moon's place was at that time near
20' forwarder in her orbit than the tables give it. Theſe two eclipfes are a
ftrong proof that the moon's place was fo much forwarder in her orbit than
by the tables as has now been faid; becauſe the beginnings of them were ma-
a ap. Ptolem. 7. 3. c. 2. b Ptolem. 1. 7. c. 2. c Ptolem. 1. 7. c. 3. d Phil. tranf. n. 492.
nifeftly
>
CHAP. 5.
435
ASTRONOMY
nifeftly one before the fetting the other before the rifing of the moon, circum- FIG.
ſtances about which the obſervers could not be miſtaken: whereas, had the
times of them been expreffed by ſetting down only the hour of the night, it
might have been pretended that the ancients had no certain method of know-
ing the time exactly, or that we could not be ſure the numbers had come
down to us without any alteration by careleſs tranſcribers. Indeed Struyck
ſeems to have been fenfible that theſe eclipſes, as they are related by Ptolemy,
are decifive in favour of Halley's opinion, which made him have recourſe
to the ſhifts before mentioned.
Again, by an eclipfe of the fun obferved at Alexandria by Theon, the 16th
day of june in the year of Chrift 364, the moon's true place was then a-
bout 4 minutes forwarder than by the tables; and confequently her motion
was then ſtill flower than the tables make it, but the difference is much leſs
than at the ancient eclipfe above 700 years before: on the other hand, in two
ſolar eclipſes obſerved by Ibn Junis at Grand-Cairo in Egypt, in the years
of Chrift 977 and 978, the true place of the moon was more backward in
her orbit than her place computed by the tables 7 or 8 minutes of a degree:
in the 63 figure, let a be the moon's place at the time of the epoch, b her 63
place by obfervation at the time of the eclipſe A. D. 977, c her place at that
time by the tables, it is manifeſt that the moon's true motion during the in-
tervening interval was the arc bcdea, whereas her motion by the tables du-
ring that interval comes out a lefs arc cdea. Now from the fame tables re-
preſenting the moon's place more backward than her true place in ancient e-
clipfes, and more forward than her true place in later eclipfes, it follows
that her motion in ancient times was flower, in later times quicker than
the tables give it us.
The difference between the places of the moon by obfervation in the eclip-
fes above mentioned and her places by the tables feem fufficient to prove that
the moon's motion from the fun has been accelerated: there is another eclipſe
of the moon, and that the moſt ancient one whereof we have any good ac-
count, obſerved at Babylon in the year before Chrift 721 march the 19th,
by which the acceleration of the moon's motion from the fun is in fome meaſure
limited: the beginning of this eclipſe is ſaid to have been an hour after the
rifing of the moon; which is not above an hour and three quarters before the
beginning by the tables: from whence it follows, that the moon's true place
at that time could not be forwarder than her place by computation much a-
bove 50 minutes of a degree.
1076 If the motion of the moon from the fun be accelerated, that is, if
the fynodical month deſcribed § 957,958, appears ſhorter now than in ancient
times
436
BOOK 3.
ASTRONOMY
times, as confifting of a lefs number of minutes, feconds, &c, this muſt be
owing to one or more of theſe cauſes; either 1, the annual and diurnal motion
of the earth continuing the fame, the moon is really carried round the earth
with a greater velocity than heretofore: or 2, the diurnal motion of the
earth and the periodical revolution of the moon continuing the fame, the an-
nual motion of the earth round the fun is a little retarded; which makes the
fun's apparent motion in the ecliptic a little flower than formerly, and, con-
fequently, the moon in paffing from any conjunction with the ſun ſpends
lefs time before the again overtakes the fun, and forms a fubfequent conjunc-
tion: in both theſe caſes, the motion of the moon from the fun is really ac-
celerated, and the fynodical month actually ſhortened: or 3, the annual mo-
tion of the earth and the periodical revolution of the moon continuing the
fame, the rotation of the earth round its axis is a little retarded; in this cafe,
days, hours, minutes, feconds, &c, by which all periods of time muſt be mea-
fured are of a longer duration, and confequently the fynodical month will
appear to be ſhortened, though it really contains the fame quantity of ab-
folute time as it always did. When we ſay the moon's motion is accelerated,
we would not be understood to determine from which of the caufes now
mentioned fuch acceleration does arife. If the quantity of matter in the bo-
dy of the fun be leffened by the particles of light continually ftreaming from
it, the motion of the earth round the fun may grow flower: if the earth in-
creaſes in bulk, the motion of the moon round the earth may be quickened
thereby. Some are of opinion that the earth may increaſe in bulk by abſor-
bing the particles of light which are continually falling upon it, or may re-
ceive an acceffion of matter from the tail of a comet. May not the motion
of the moon round the earth have been quickened, or the motion of the
earth round the fun have been retarded, by the near approach of a comet?
but more of this when we come to enquire into the cauſes of the motions of
the planets.
CHAP. 6.
THE HARVEST MOON: THE HORIZONTAL MOON.
1077 It is a common obſervation that, about the latter end of july, in au-
guſt, and the beginning of feptember, the moon, when juſt after the full,
rifes feveral nights together foon after the fun fets; fo that, by fucceeding the
fun before the twilight is ended, the moon prolongs the light, to the great
benefit of thoſe who have harveft work to do, and is therefore called at that
time the harveſt moon: how this comes to pafs is now to be explained. As
the
CHAP. 6.
437
ASTRONOMY
the rotation of the earth cauſes all the heavenly bodies to appear to riſe and FIG.
ſet in the equator, or in a circle parallel to the equator, § 343, the moon muſt
every day riſe and fet in the equator, or in a parallel: let fig. 64, repreſent 64
a view of the eaſtern concave hemifphere of the heaven, wherein N is the
north s the fouth pole, E Q the equator, H R the horizon of a place in the
latitude of Cambridge, and will not be much amifs, as to the affair under
our preſent confideration, if we make it the horizon of any other part of Eng-
land: it is eaſy to ſee that if the moon be in the equator as at A or B ſhe muſt
in this hemiſphere appear to be carried towards Q, and that ſhe comes to the
horizon and riſes at : but if ſhe be in a parallel p p as at a or b or c ſhe ap-
pears to be carried in that parallel towards p, and riſes at h.
1078 Lemma 1. If two points both in the equator as A and B fig. 64, or 64
both in the fame parallel as a and b be taken in the eaſtern hemiſphere un-
der the horizon, the point nearest to the horizon muſt riſe firft: thus, the
point A rifes before в: in like manner в rifes before c, and c before D, as
alſo a before b, and b before .c &c: how much в riſes later than A, or b later
than a, in a right ſphere, depends upon the difference between the right af
cenfions of thoſe points; in an oblique fphere, upon the difference between the
oblique afcenfions of them: this difference is in both caſes the fame; for it is
the arc of the equator contained between A and B, or the arc of the parallel
contained between a and b: thus, if the arc A B contains 15 degrees, в muſt
come to the horizon N s in a right fphere, or to the horizon HR in an ob-
lique ſphere, an hour later than A: in like manner, if the arc a b contains
15 degrees, a muft, both in a right and oblique fphere, rife an hour before
b; for as every point in the equator appears to go round in that circle in a
natural day, fo does every point in any parallel go round in that parallel in
the ſame ſpace of time: the degrees in every parallel are indeed leſs than thoſe
in the equator, but an arc of any number of degrees in a parallel bears the
ſame proportion to that parallel as an arc of the fame number of degrees in
the equator bears to the equator, § 484; and confequently takes up the fame
interval of time in paffing through the plane of the horizon, or of any other
circle.
Corollary. The lower the moon is under the eaſt part of the horizon the
later muſt ſhe rife, in the fame pofition of the ſphere.
1079 Lemma 2. Since in every place in north latitude the north pole is
above the horizon, the fouth pole is below it, if when any of the heavenly
bodies is beneath the horizon in the eaſtern hemiſphere it is deviating north-
ward it will by fuch deviation be brought nearer to the horizon, and con-
fequently riſe fooner than it would otherwiſe do: thus, fig. 64, if the moon 64
3 K
at
438
BOOK 3.
ASTRONOMY
FIG. at A inſtead of going to B in 24 hours were in that time to go an equal di-
64 ſtance from A to f, this deviation would leffen the change of her oblique af-
cenfion, which would then be no more than v g; and ſhe would rife at F, as
much fooner than fhe would have done had fhe gone to в as anſwers in time
to the difference between the arcs v g and v B: it is obvious that a deviation
fouthward as from A to a has a contrary effect, carries any of the heavenly
bodies farther beneath the horizon, and caufes it to rife later.
1080 It is matter of common obfervation that the moon, in going round
her monthly period, rifes and fets every natural day later than ſhe did on the
day immediately preceeding. When the moon is in conjunction with the fun ſhe
rifes and fets nearly at the fame time as the fun does, and is fo near the fun
as to be invifible, § 967, 970: in a day or two, the moon will be at ſuch a di-
ftance from him as to be viſible in the weft after the fun is down; at this firſt
appearance fhe is commonly called the new moon: from thence forwards
the moon, advancing farther and farther from the fun, riſes every day later,
and later after fun-rife, and fets later and later after fun-fet, till fhe comes
to be in oppofition to the fun: during this half of the month, the rifing of
the moon is in the daytime, and is therefore but little regarded, except per-
haps by aftronomers; the time of her ſetting is then principally attended to,
in order to know how long, after the fun is down, ſhe will continue to fup-
ply his place with her borrowed light.
When the moon is in oppofition to the fun or at the full ſhe rifes nearly at
the time the fun fets, and fets nearly at the time the fun riſes: from thence
forward, fhe every day rifes later and later after funfet, and fets later and later
after ſunriſe: during this half of the month, the ſetting of the moon, being
in the daytime, is not attended to, for common uſe; the time of her rifing is
then chiefly enquired after, in order to know how foon, after the fun is gone
down, ſhe will appear and diſpell the darkneſs of the night.
1081 The cause of the moons rifing and ſetting later every day than on
the day immediately preceding is her going in her orbit according to the or-
der of the figns about 13 degrees every 24 hours, which is about 12 degrees
farther than the fun goes in the ecliptic, as has before been mentioned,
$958: by this motion of the moon, at whatever hour and minute ſhe is at
the horizon ready to rife on a given day, at the ſame hour and minute of the
day immediately following fhe will have been carried more or lefs beneath
the horizon; her oblique aſcenſion will have been changed, and confequent-
ly ſhe muſt rife as much later as anſwers to the exceſs of that change, above
the change of the funs right aſcenſion in the ſame time, by § 1078.
1082
page 439.
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Book III.
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Ap
CHAP. 6.
439
ASTRONOMY
1082 The difference in the times of the rifing of the moon on days immedi- FIG.
ately ſubſequent is variable: when this difference is greateſt, the moon rifes
almoſt an hour and an half later in the day than on the day immediately pre-
ceding: when this difference is leaſt, the moon does not rife 12 minutes later
in the day than on the day immediately preceding.
The cause of this variableness in the rifing and ſetting of the moon is the
different fituation of the moons orbit in reſpect of the horizon of the place
under confideration: for in fame fituations thereof the oblique afcenfion of the
moon fuffers a greater change in any given time than it does in other
fituations.
1083 As about one half of the moons orbit is on the north the other half
on the fouth fide of the ecliptic, § 955, it will not be improper firſt to con-
fider the motion of the moon as if it were always in the ecliptic.
The ecliptic, in different fituations of the heaven, makes different angles
with our horizon, and indeed with the horizon of every place, as may be
feen by turning about the celestial globe: thus, if the globe be rectified to our
horizon, and turned till the point of the ecliptic be under the braſs me-
ridian, the ecliptic will ftand the neareſt poffible to perpendicular to our
horizon, making with it an angle of about 61 degrees, which is the greateſt
angle it can ever make with our horizon: on the other hand, if the globe
be turned till the point w be under the meridian, the ecliptic will be the
neareſt poffible to coincidence with our horizon, making with it the ſmall-
eft angle poffible, an angle of no more than about 14 degrees.
On any day of the lunar period, when, a little before the rifing of the
moon, the ecliptic makes the greateſt angle poffible with our horizon, the
motion of the moon in the ecliptic, as for the prefent we fuppofe it to be,
will, during the preceding 24 hours, have carried her the fartheft poffible
beneath the horizon, and there will be the greateſt change made in her ob-
lique afcenfion, ſo that there will then be the greateſt difference between the
time of the moon's rifing on that day and the time of her rifing on the day im-
mediately preceding: on the other hand, when on a given day, a little be-
fore the rifing of the moon, the ecliptic makes the leaft angle poffible with
the horizon, the motion of the moon during the preceding 24 hours will
have made the leaft change poffible in her oblique afcenfion, the will be but
a little below the horizon, and confequently there will then be the leaſt dif-
ference between the times of the moon's rifing on that day and on the
day immediately preceding. Let fig. 65, 66, 67, 68, 69, be views of the 65
concave eaſtern hemifphere of the heaven, in each figure N is the north s 66
the ſouth pole, E Q the equator, H R the horizon, the ecliptic, wherein
3 K 2
the
{
440
воок 3.
ASTRONOMY
FIG. the moon is fuppofed to move according to the order of the letters A B C D;
on a given day and hour, for example, the 21 of june at noon, let the
65 ecliptic ftand as in fig. 65, with the moon rifing at ; on the following
day at noon the moon will be about 13 degrees forwarder at c, and muſt
then riſe at F, in the parallel Pcp, as much later than on the 21 day as
anſwers in time to the arc FC, equal to the change of her oblique aſcenſion
above the change of the fun's right afcenfion: if that excefs be 18 degrees,
66 ſhe will on the 22 day riſe at 12 minutes past one. On the other hand, let
the ecliptic ftand as in fig. 66 at noon on a given day, as december 21, with
the moon rifing at r; on the following day at noon fhe will be at c, and
rife at F, in the parallel Pcp, only as much later in time than on the pre-
ceding day as anſwers to the arc Fc: if that arc be 5 degrees, fhe will riſe
20 minutes past twelve. It is eaſy to ſee that, between theſe two extreams,
there are various fituations of the heaven, wherein the ecliptic cuts the
horizon at intermediate angles, between the greateſt and the leaſt; and, con-
fequently, that the differences between the times of the moon's rifing on two
days immediately ſubſequent are various. To exprefs the matter in ſhort,
the nearer to perpendicular to the horizon the ecliptic is, the farther would
the motion of the moon therein carry her under the horizon.
1084 The differences which have been mentioned between the rifing of
the moon on days immediately fubfequent happen to the moon in all her
phaſes; but the rifing of the moon near the fame hour for feveral evenings
together is chiefly taken notice of after the full moons which fall out a little
before the autumnal equinox: becauſe the days feem to be thereby moſt be-
neficially lengthened, as there is then no interval of darkneſs between the
ftrong twilight and the rifing of the moon.
From about the middle of auguft to about the middle of feptember new-
ftile, the fituation of the ecliptic at funfet is nearly fuch as is repreſented in
66 fig. 66; fuppofe then on the 15th of auguft at funfet the full moon is ri-
fing at B, on the 16th at ſunſet ſhe will be at c, fo near the horizon that,
being by the diurnal motion carried in the parallel Pcp, fhe will riſe at F,
not many minutes after the time ſhe roſe on the 15th; for the change of her
oblique afcenfion, during the intervening 24 hours, is no more than the
fmall arc CF; on the 17th at funfet, the moon will be at D, on the 18th at
&c. all which points are ſo near the horizon that, though for ſeveral days
following the moon riſes later and later every day, her rifing is all the while
ſo ſoon after the ſetting of the fun that the appears before the twilight, which
then continues about two hours after funfet, is grown ſo faint as not to be
ferviceable to the induſtrious farmer.
1085
CHAP. 6.
441
ASTRONOMY
1085 In places of greater north latitude than Cambridge, when the point FIG.
is in the meridian, the ecliptic is nearer coincidence with the horizon, and
confequently their harveſt moon riſes ſooner after ſunſet than at Cambridge.
If a place be in 66 degrees and an half of north latitude, when the point b
is in the meridian, the ecliptic is coincident with the horizon; in every fuch
place the moon rifes for above a week together at the fame time the fun fets:
thus, fig. 67, if the ecliptic be coincident with the horizon at ſunſet 67
on a given day when the moon is rifing at A, on the day following the will
be at B, on the third day at c, on the fourth at D, &c: now all thefe points
will on each of theſe days at ſunſet be in the eaft fide of the horizon ready
to rife at the fame time that the fun is on the weft fide of the horizon ready
to fet.
1086 It has been faid before § 952, that the moon's motion in her orbit
is not equable, but floweſt in apogee, ſwifteſt in perigee: it is eaſy to ſee
that the fwifter the motion of the moon is in her orbit the greater change is
made in her oblique afcenfion in a given time, and confequently cæteris pa-
ribus the later, will fhe rife; the flower her motion is in her orbit the leſs
is the change made in her oblique aſcenſion in a given time, and the fooner
will fhe rife. From hence follows this corollary, that cæteris paribus, the
leaſt interval of time between the ſetting of the fun and the rifing of the har-
veft moon, is when the moon is in apogee.
1087 As the moon does not go in the ecliptic, but in an orbit that cuts
that circle in an angle of about 5 degrees, $955, the orbit of the moon, in
one fituation, makes an angle with the horizon 5 degrees larger, in another
fituation, an angle 5 degrees lefs than the ecliptic can ever do: thus, fig. 68, 68
the pointed line мm, which repreſents the orbit of the moon cuts the hori-
zon HR, ſo as to make with it an angle of 66 degrees, 5 degrees larger than
the ecliptic does. On the other hand, in fig. 69, the orbit of the 69
moon мm makes an angle with the horizon HR, of 9 degrees, 5 degrees leſs
than the ecliptic does. In fig. 68, the moon going in her orbit mm accord- 68
ing to the order of the letters abcd, deviates towards the fouth; and therefore
rifes the later: in fig. 69, the moon deviates towards the north, and therefore 69
riſes the fooner for fuch deviation, by § 1079. When the moon is at the
full and ready to riſe at ſunſet, if the ecliptic and the orbit of moon ſtand
both as in fig. 69, and the moon is alfo in apogee, there will be the leaſt 69
difference poffible in our latitude, between the times of the moon's rifing on
that day and on the day immediately preceding; fo that we ſhall have the beſt
harveſt moon that ever we can have, by § 1079, and 1086.
Scholium.
442
BOOK 3.
ASTRONOMY
appear
Scholium. The refraction of the air near the horizon makes the fun
to fet later, and the moon to riſe fooner than they really do: refraction
therefore ſhortens the interval of time between the ſetting of the fun and
the rifing of the moon. Refraction is variable, the more denſe the air is
when the moon is ready to rife the greater is the refraction, and the fooner
will the moon appear above the horizon, other circumſtances being the
fame.
1088 It is a common obſervation that the horizontal moon or the moon
near the horizon appears much larger than when near the meridian; what
makes this fo difficult to account for is that we are very fure the moon
is not nearer to us in the former than in the latter fituation: in reality ſhe is
nearer to us in the meridian, as was faid § 1041; but this difference in her
diſtance, though neceffary to be taken notice of in nice aftronomical calcu-
lations, is too ſmall to caufe any change in her apparent magnitude eſti-
mated by the bare eye, and therefore needs not be regarded in the preſent
fpeculation, wherein we may confider the moon as if he were all the while
at the fame diſtance from us, and appeared conftantly under the fame
optical angle.
appears
1089 Various are the folutions given of this phenomenon, one is that
the pupil of the eye is opened wider, and by that means a larger picture of
the moon is painted upon the retina, § 229, when ſhe is viewed near the ho-
rizon, her light being then much obfcured by the great quantity of thick
vapours through which it paffes; whereas when ſhe is at a greater altitude
her light comes to us through a ſhorter tract of thinner air, and ſhe
brighter, which cauſes the pupil of the eye to be contracted and her picture
upon the retina to be diminiſhed: this reafoning is founded upon a fact
which is not true; for, though the pupil of the eye is enlarged in the dark,
and contracted in the light, and is alſo opened wider when we look at a
dark object than when we view the fame ftrongly illuminated, this change in
the pupil cauſes no alteration in the apparent magnitude of the thing feen:
and accordingly we find the moon at a confiderable altitude does not appear
larger when feen through a cloud, or even when eclipſed, than in her great-
eſt brightneſs: nor ſhall we find any difference in her apparent magnitude at
any time, whether we view her ſtanding in clear moonshine, or retire into
a dark room: though the pupils of our eyes will be more contracted in the
former than in the latter fituation.
1090 Another opinion is that the horizontal moon being feen through a
long tract of thick vapours her picture upon the retina is confufed, becauſe
the pencils of rays which come from the outlines of her difk do not termi-
nate
CHAP. 6.
443
ASTRONOMY
nate in points but in ſmall circles, which renders the picture ſo much larger FIG.
in circumference as the femidiameters of thoſe circles extended every way
round amount to; but that, when a micrometer fitted to a teleſcope is made
uſe of, the glaffes correct this diffipation of the pencils, and the moon ap-
pears under her true angle, a little lefs in the horizon than in the meridian.
Now that this is not the cafe, is evident from the following experiment, up-
on one end of a ſquare ſtick about 6 feet long fig. 70, I fixed a thin brafs
70
plate A with a ſmall hole, and near the other end I placed a fliding frame в
which carried two parallel wires about half an inch diftant from each other,
then looking through the hole in the braſs at the moon near the horizon,
and directing an affiſtant to move the fliding frame till the wires appeared
juſt to claſp her difk; I made the fliding frame faſt, and ſome hours after
looking in the fame manner, at the moon riſen to a greater height, I found
her diſk did then extend beyond the wires: thus, by this inftrument which
may be called a micrometer without glaffes, the horizontal diameter of the
moon was found to meaſure larger, or fubtend a greater angle the greater
her altitude was.
1091 The two folutions now mentioned ſeem to be founded upon an o-
pinion that our judgment of the apparent magnitude of an object is formed
folely from the optic angle; now this is true only with regard to fuch objects
as are at equal diſtances, or appear to be at equal diſtances from us, which
they may do by reaſon of their being fo remote that we have no means to
eſtimate their diſtances or compare them together, as is the cafe of the fun and
moon § 248; whereas our eſtimation of apparent magnitude is made by the
optic angle and the ſuppoſed diſtance of the object confidered together, in
all cafes wherever that diſtance is by any means fuggefted to the imagi-
nation, whether 1, by the fituation of the thing viewed among other things
which appear near it, or 2, by the extenſion of ſpace between us and the ob-
ject, (which perhaps is meaſured by the time the eye takes in travelling over
it, for though the eye runs over a very large ſpace with a velocity as quick
as thought, yet it takes up more time in doing it the farther the ſpace is
extended; just as the greater number of ideas fucceed one another in the
mind the more time is taken up by them, how quick foever that fucceffion
be:) or 3, by the number of objects feen between the eye and the thing in
view, or laſtly, by the colour, diftinctneſs or confufion of its picture; for we
have learn'd from experience that when certain known things have appeared
in fuch or ſuch circumſtances they have been at ſuch diſtances from us;
now this connection is laid up in the mind, quiefcens eft in anima, fays Alhazen,
as
444
BOOK 3.
ASTRONOMY
FIG. as he is tranflated by Gerardus Cremonenfisa, fo that, whenever an object
is feen, the idea of diftance connected with thofe circumftances which attend
it is excited in the mind, and that ſo inſtantaneouſly that we cannot diſtinguiſh
between the judgement we make and the perception of the ſenſe; but think
we ſee a thing at fuch a diſtance: whereas diftance is not a thing feen; for
the eye receives nothing but the picture made by the particles of light re-
flected from the body we look at, § 229.
It has before been obferved § 248 249, that all the heavenly bodies ap-
pear to be at the fame diſtance from us, and that to the eye they ſeem all
to be placed in that concave furface which I call the fphere of the heaven:
the vifible part whereof, though properly enough called an hemifphere,
becauſe we have always half of this fphere above our horizon, ap-
pears in ſhape of a fegment or part of a ſphere, the center whereof is
70 far below the eye: thus, fig. 70, let a be the place of the ſpectator, the
vifible part of the ſky, whether all over blue as in clear weather, or co-
vered with clouds appears in the fhape reprefented by the curve ABC;
ſo that the parts of the ſky at c over his head feem to be neareſt to him,
and all the other parts of it more and more diftant, down to the horizon
B or D.
a
1092 This apparent figure of the sky is fixt in our imagination, and is
owing to feveral caufes, as firft, to the extent of ground and the number of
objects we often ſee between us and the horizon, whereby we make fome eſ-
timation of the meaſure of its diſtance; whereas we have nothing between
us and the ſky over our heads to meaſure with, and therefore that part ſeems
nearer to us: 2, the part of the fky near the horizon feems to be farther
from the eye, becauſe it appears lower, as was obſerved of the
parts of
cieling § 247: if a man had over his head a cieling which extended direct-
ly from before him as far as he could fee, the parts of it would ſeem gra-
dually lower as they grew farther off, till the fartheft vifible part appeared
to touch the horizon: now if we imagine this cieling to be extended every
way round, every part of it would feem lower and lower the farther it
was off, till the fartheft part vifible quite round appeared to touch the
horizon. When the ſky is all over uniformly covered with clouds we have in
effect the ſame thing as the cieling now fuppofed, thoſe clouds that are fartheſt
off appear loweſt, and, vice verfa, thofe that appear loweſt appear fartheſt
off; and in reality are fartheft off: it is probable we thus come by the idea
a Alhazen Optices, 1. 2. prop. 24.
we
CHAP. 6.
445
ASTRONOMY
we have of the ſhape of the ſky, as Dr. Smith, has obferved in his optics p. 63. FIG.
The height of clouds above the furface of the earth we may ſuppoſe at a me-
dium to be about one mile; the height of many clouds is not above half a
mile: thoſe perſons who have been upon the tops of very high mountains
have generally, in that fituation, found themſelves above the clouds, which
they have ſeen floating in a lower region of the air: there muſt indeed be
fome clouds which rife much higher, if we reckon their height from the
furface of the ſea; as, for inftance, thoſe which carry fnow unto the
top of the higheſt alps, mentioned § 576: perhaps the wind, blowing against
the floping fide of an high mountain, may ſometimes drive fnow over the
top thereof, from a cloud that is not quite ſo high.
1093 It appears by the tables p. 133, that, if the diſtance of an object be
three miles, the height of the apparent level is near 8 feet: converſely
then, if the eye be 8 feet high above the ſurface of the earth, the extent of
the visible horizon will be about 3 miles: refraction extends it a little far--
thera: we judge the diſtance of clouds near the horizon to be much the fame
as that of the moſt diſtant parts of the earth within our view, to which they
appear contiguous: thus, in fig. 71, let BCD repreſent the ſky covered with
clouds within the vifible horizon of a ſpectator at A, AC is about one
mile, AB or AD about 3 miles. If we confider the ſky without clouds, it
is formed of the air, or that part of our atmoſphere which is within our vi-
fible horizon; our atmoſphere may be conceived to confift of an indefinite
number of ſpheres of air, all concentric to the earth: the air is more denſe
the nearer to the earth; and the denfer the air is the heavier particles of mat-
ter will be ſupported therein: what we call the blue ſky is formed by par-
ticles of matter fo fmall that they reflect only the blue-making rays of light,
which are moſt reflexible, the rays of other colours being tranfmitted b: theſe
ſmall particles are buoy'd up higher in the atmoſphere than they can be when
they coalefce into larger ones, fo as to form clouds: what ever the height of
the blue-reflecting particles may be, we have nothing to meaſure it by; and
therefore, from the apparent figure of the ſky all over cloudy, we form our
idea of the figure of the ſky when interſperſed with clouds, or even when
quite clear of them: what we call the blue ſky appears only a little farther
off than the clouds, and, when cleareft, is always diluted with a whiteneſs near
the horizon, which makes thoſe parts appear a little nearer to us than other-
wife they would do: in effect, the blue ſky is a ſmall ſegment of a ſphere
a § 295. b Newton's optics, part 2. prop. 7.
3 L
not
71
446
BOOK 3.
ASTRONOMY
FIG. not much larger than the fky all covered with clouds; to this ſky, the ſhape
whereof is fixed in our imagination, we refer the moon and ſtars in a clear
night; and fee them as if they were placed therein.
1094 Dr. Smith by ſeveral obfervations, found the horizontal line A B or A D
in the figure of the ſky to be between three and four times the length of the
71 perpendicular line AC; hence it comes to paſs that the moon when near B or
D appears between three and four times as large as when near c, though
feen nearly under the fame angle in both fituations, becauſe we judge her
diſtance to be three or four times greater at D or B in the horizon than
at c in the zenith.
1095 Another caufe of the parts of the ſky feeming more diftant the nearer
to the horizon is this, the heavenly bodies appear more confuſed and indiſtinct
the nearer they are to the horizon, which fuggefts to the mind the idea of greater
diſtance both of thoſe bodies and of the fky wherein they appear to be placed.
Now that we form this judgment of the heavenly bodies is owing to the
experience we have of bodies upon the earth, which always appear more
indiftinct, the greater their diſtance is from us, § 246: the cauſe of this it is
eaſy to affign, from what was ſaid §747, that the ſmall particles of mat-
ter which float in our atmoſphere reflect light; and confequently, the farther
diſtant any object is from the eye, the greater number of thoſe particles will
the rays of light which ſhould make it diſtinctly viſible meet with, in their
paffage towards us; and the greater number of thoſe rays muſt thereby be
intercepted, refracted, and reflected: efpecially, if the object be ſeen near the
horizon, as all diſtant ones upon the earth are; for then it is feen through
that part of the air which is moſt denſe and fulleſt of thick vapours.
Scholium. For the fame reafon the diſtance of two ftars near the horizon
appears between 3 and 4 times as great as when the fame ftars are near the
zenith. The horizontal moon fome times appears larger than at other times,
though at the fame diſtance from the earth, and therefore ſeen under the
fame angle: this is owing to the different denfity of the atmoſphere, which
cauſes a difference in refraction, and confequently varies the extent of the
vifible horizon, as was obſerved § 295.
Remarks upon § 1090..
1096 When a luminous body appears confufed, the picture of it upon
the retina is a little larger than when it appears diftinct: becauſe, in the for-
mer cafe, the pencils of rays which come from the extream points or out-
lines
CHAP. 7.
447
ASTRONOMY
lines of the object terminate in ſmall circles; whereas, in the latter cafe they
terminate in points: this would explain the phenomenon of the horizontal
moon, if the appeared only a little larger near the horizon than in her great-
eft altitude; but will by no means account for the great difference that every
one may obſerve in the apparent magnitude of the moon, in thoſe different
fituations.
What the pencils of rays are was explained in the introduction, from
§ 225 to § 235: I fhall only add that in the experiment of the camera obſcura
mentioned § 230, &c. every pencil of rays paffing through a lens terminates
in a point at a certain diftance, at which when the paper is placed the pic-
ture is diſtinct; whereas, if the paper be placed nearer, the pencils terminate
in fmall circles which interfere with one another, ſo that ſome of the rays
of different pencils fall upon the fame part of the paper, and cauſe confufion
in the picture: the fame will alſo happen if the paper be placed too far from
the lens, the pencils will then alſo terminate thereon in circles; becauſe in
every pencil the rays, which proceed converging till they come to a point,
there croſs one another, and thence proceed diverging: notwithſtanding the
place of the diſtinct picture is not ſo confined to a certain exact diſtance as not
to allow of ſome ſmall latitude; for, by reafon of the different refrangibility
of the rays of light mentioned § 218, the rays of the fame pencil, being of
different colours, will not all converge to a point exactly at the fame diſtance
from the lens, as they would do if they were all of the fame colour: the
picture is then moſt diſtinct, when the paper is at ſuch a diſtance from the
lens as to have the greateſt quantity of rays in each pencil converge to a point
thereon: this is alſo the propereſt diſtance for burning with a convex glaſs.
The fame rule is alſo applicable to diſtinct vifion: the eye is capable of
confiderable changes, in the form and fituation of its parts; otherwiſe, we
could not fee diſtinctly at fuch various diſtances as in fact we are able to do:
thoſe changes may be made either by our altering the figure of the humours
of the eye, or by bringing the retina nearer to the pupil, or removing it
farther from it. Jurin's effay, in Smith's optics, vol. 2.
eſſay,
CHAP. 7. THE MOONS OR SATELLITS OF JUPITER.
1097 Jupiter bath four moons or fatellits, which, continually revolving round
him according to the order of the figns, in orbits of different diameters,
and in different periods of time, accompany him in his twelve years re-
volution round the fun; in the fame manner as the moon attends our
earth,
3 L 2
448
BOOK 3.
ASTRONOMY
earth, in her annual revolution through her orbit. Three of them were firſt
feen by Galileo, on the night of the 7th of january A. D. 1610, who then
took them for teleſcopic ſtars, but, by the obſervations of three or four
fubfequent nights, difcovered them to be attendants upon the planet ju-
piter: on the 13th of the fame month he faw the fourth fatellit, and con-
tinued to fet down the various configurations of them with their primary,
every night that was clear enough to let them be feen, till the fecond of
march following: on the twelfth of the fame month, he fent his drawings
of them to his patron Cofmo Medici Great Duke of Tuſcany; in honour
of whom he called them Medicean ftars: from that time, he was fo at-
tentive to their motions, that, at the end of the year 1612, he printed
ſchemes of the ſeveral fituations in which they would appear at feveral dif-
ferent hours every night of the months of march and april, and to the
eighth of may in the year 1613, together with an account of fome of their
eclipfes by the ſhadow of jupiter; beſpeaking the candor of his readers, in
cafe he fhould be a little out in fome of his predictions, as the ſubject was
new, and thoſe ſtars might have fome irregularities not diſcoverable in fo
fhort a time b
1098 It was foon underſtood how uſeful thoſe ſatellits might be made in
finding out the longitude, if exact tables of their motions could be conſtruct-
ed; in order to this, Galileo continued his obfervations of them for 27
years, till the lofs of his eye-fight hindred him from proceding any farther:
but the fruit of thoſe labours was loft, though the Dutch fent Hortenfius,
Bleau and other mathematicians to affift him in his obſervations and calcu
lations: at the fame time, feveral other aftronomers were employed in the
fame defign, in various places; with what fuccefs may be ſeen in Caffini,c
who mentioning Borelli among the reft, treats him with leſs regard than
I think his performance deferves: that author in the year 1663 printed the
theory of the Medicean planets in two parts: in the firſt of which, he ſup-
poſes the fatellits of jupiter to be carried round him in elliptic orbits, of dif-
ferent diameters, and in different planes, in like manner as the primary pla-
nets are round the fun, and from the fame cauſes; namely gravitation towards
their primary, and a centrifugal force arifing from their being whirled round
a They are now ufually called the firft fecond third and fourth fatellit, according to the different dif-
tances of their orbits from their primary: the firſt ſatellit is that which is carried round at the leaſt diſtance
from jupiter.
b Nuntius fidereus & iftoria e dimoftrazione intorno alle macchie folari in Roma, 1613.
c Les hypothejes et les tables des fatellites de jupiter.
their
page 449
d.
72
M L
N
Book III.
a
73
b
85
a
F
-E
B
1
75
a
a
76
77
}
b
78
74.
A
79
D
G
80
UNI
FICH
a
M
СНАР. 6.
449
ASTRONOMY
their primary: he ſuppoſes alſo that the inclinations of the planes of the or-
bits of the fatellits to the plane of jupiters orbit, their excentricities, the po-
fitions of their longeſt axes, and the places of their nodes are all ſubject to
the like changes as in the orbit of the moon, but in different quantities. In
the ſecond part, he propoſes methods of inveſtigating theſe elements, fuggeſts
feveral cautions to be uſed in obſerving, and gives a few obſervations made
by himſelf and others, which he thought confirmed the truth of his ſuppo-
fitions; but refers the farther diſcovery of the exact theory of theſe planets
to pofterity, as a difficult work, not to be accompliſhed but by many years
diligent obſervation.
1099 In the year 1668, Caffini publiſhed tables of the motions of jupiters
Satellits, but much more compleat ones in the above mentioned work printed
in 1693, wherein he gives directions for the uſe of his tables, after premiſing
a long detail of the pofitions and diameters of the orbits of the fatellits, their
mean motions, and the manner or inveſtigating theſe particulars: the orbits of
jupiters fatellits were thought by Galileo to be in the fame plane with the or-
bit of jupiter: Caffini found them to make a ſmall angle with it, and, not
being able to diſcover any difference in the places of their nodes, conclud-
ed them to be all in the fame place, and that their afcending nodes were about
the middle of : after having obſerved them above three twelve years peri-
odical revolutions of jupiter, he found their greateſt latitude or deviation from
the plane of jupiters orbit to be 2° 55.
AAN
C
The tables of Caffini have been corrected by Dr. Halley,a Mr. Pound,
the French Aftronomers, and,Dr. Bradley. The diſtances of theſe fatellits
from the center of jupiter are meaſured by the micrometer; and computed
either in femidiameters of jupiter and decimal parts, or in minutes and fe-
conds of a degree: in the following table the diſtances are fet down in both
thofe methods, together with the periodical times in which the fatellits are
carried round their primary. v. Newtoni principia, lib. 3. phænom. 1.
days hou.
"
I
the
diſtance
of the
2 fatel-
3
lit
jupiter is
4
in femidi- 5-697 in minutes
ameters of 9.017 and feconds
14.384
25.266
2 56
of a degree is
4 42
8 16 is
51″ peri- 1 18 27 34
odical 3 13 13 42
time 7 342 36
16 16 32 09
a Lowthorp's phil. trans. abr. vol. 1. p. 409. b Jones's phil. trans. abr. vol. 4. f. 308.
c Memoires d'Acad. 1727 M. Caffini elements d' aftronomie, liv. 9. et tables aftronomiques p. 153.
d Phil. trans. n. 394. & in appendice ad Halleii tabulas aftronomicas in 4to Londini A. D. 1740.
I IOO
450
BOOK 3.
ASTRONOMY
FIG. 1100 The orbits of jupiters fatellits are not all in the fame plane, nor are the
nodes of them all in the fame place. The plane of the orbit of every fatellit
of jupiter extended would cut the heliocentric orbit of its primary in two
oppofite points, which are called the nodes or the true nodes of the fatellit:
the afcending node of a fatellit is that through which it paffes in going into
north latitude; the defcending node is that through which it paffes going
into fouth latitude from the orbit of its primary. Two points taken in the
orbit of a fatellit at equal diſtances from each node are called the limits of
the fatellit: theſe points mark the places of its utmoſt deviation from the orbit
of its primary; all this is eafily underſtood from what was ſaid of the moons
deviating into north or fouth latitude from the ecliptic, § 955.
To a ſpectator in jupiter, every fatellit, when in either of its nodes, would
appear in the heliocentric orbit of its primary; in every other ſituation, it
would be in north or fouth latitude from the orbit of its primary. The plane
of the orbit of every fatellit extended would alfo cut the ecliptic in two oppofite
points, which, to diſtinguiſh them from the true nodes, may be called its
geocentric nodes.
1101 When the earth is in one of the geocentric nodes of a fatellit, the plane
of its orbit extended paffes through the eye of an obſerver upon the earth;
and, therefore, if viſible, it would then appear to be a ftrait line, § 258 and
72 265, fig. 72: in every other ſituation of the earth, the orbit of a fatellit, if vi-
fible, would to an obferver upon the earth appear as an ellipfis, more or leſs
oblong, as the earth is nearer to or farther from the nodes of the fatellit, § 258:
this ellipfis when wideſt can be but a narrow one; becauſe the orbit of every
fatellit is inclined to the ecliptic in a ſmall angle, fig. 73. This fhews us
how it comes to paſs that the motions of the fatellits appear to us to be ſome-
times in ftrait lines, fometimes in elliptic curves.
73
72
73
1102 The fyftem of jupiter and his fatellits, though very large in its felf,
by reafon of its immenſe diſtance from us, appears to take up a very ſmall
ſpace in the ſphere of the fixed ftars: and therefore every fatellit of jupiter
appears to us always near its primary, and to have an oſcillatory motion,
like that of a pendulum, going alternately, from its utmoſt elongation or great-
eſt diſtance from its primary on one fide, to its utmoſt elongation or greateſt
diſtance on the other fide: ſometimes in a ſtrait line, as in fig. 72; fometimes
in an elliptic curve, as in fig. 73.
1103 When a fatellit is in its fuperior femicircle, or that half of its orbit that
is more diftant from the earth than jupiter is, its motion to us appears direct,
according to the order of the figns; when a fatellit is in its inferior femicir-
cle,
CHAP. 7.
451
ASTRONOMY
72
cle, nearer to us than jupiter is, the apparent motion of it is retrograde. Let FIG.
fig. 72 reprefent jupiter with the orbit of one his fatellits viewed from the
earth fituated in one of its geocentric nodes; when the fatellit is in its fupe-
rior femicircle, its apparent motion is direct, fom a to d, according to the order
of the letters; when in its inferior femicircle its apparent motion is retro-
grade, from d to a: again, let fig.73 repreſent jupiter and the orbit of a fatellit 73
viewed from the earth, at the greateſt poffible diſtance from the geocentric
nodes; the apparent motion of the fatellit in its fuperior femicircle, is in
the curve abcd, according to the order of the letters: in its inferior femi-
circle its apparent motion is in the curve defa. Both the direct and retrograde
motion of a fatellit appears quicker, the nearer the fatellit is to the center of
its primary; flower, the neer to its greateſt elongation: in its greateſt
elongations it is ſtationary: fe8 264 and 265.
1104 The orbit of every fatellit, though nearly circular, is not exactly fuch,
but an ellipfis, having jupiter in one of its focuſes: the point where the fatellit
approaches neareſt to jupiter is called its perijovium; where it is at the greateſt
diſtance from jupiter its apojovium. The excentricities of the orbits of the
fatellits are too ſmall to be obſerved by the micrometer; that inftrument will
not fhew
any difference between the greateſt elongations of the fame fatellit
from its primary: nor has any other method, hitherto, difcovered any of
the three innermoft to be excentric, though all of them are fufpected to be
foª. The orbit of the fourth is found to be an ellipfis, the mean diſtance
whereof being divided into 1000 equal parts, its excentricity is but a little above
of thoſe parts: the apojovium of this fatellit has a motion like that of the
moons apogee mentioned § 961, but much flower; being carried according
to the order of the figns at the rate of fix degrees in ten years
7
cle
b.
1105 Every fatellit when going towards the middle of its fuperior femicir-
may ſuffer an occultation, that is, may be hid from our view behind its pri-
mary: this is always the cafe of the firſt and ſecond ſatellit; the fourth may
fometimes eſcape being hid by its primary, which may alfo, but very rare-
ly, be the cafe of the third. A fatellit may alſo diſappear near the middle of
its inferior femicircle, as it goes between us and its primary: for the beſt te-
leſcopes will ſeldom enable us to diſtinguiſh a ſatellit upon the diſk of jupi-
ter, except at its first entrance thereon, and juft before it goes off therefrom.
In thoſe fituations, a fatellit appears like a lucid fpot,c being more directly
illuminated by the fun than the parts of jupiter near the circumference of
his diſk are; for, thofe, by reaſon of his globular figure, turn away from
a Memoires d'Acad. 1727 & 1732. b. Bradley in notis in tab, c Memoires d'Acad. 1707.
the
452
ASTRONOMY
BOOK 3.
1
FIG. the fun, and receive his rays obliquely: fo as to reflect fewer of them to us.
However, a fatellit, fometimes, in paffing over, appears lefs bright than
jupiter; and is thereby diſtinguiſhed from him: this is owing to the fatellit
having pots; that is fome parts of its furface are not fo well fitted to reflect
the light of the fun as others are. The fame fatellit has, at one time, been ob-
ferved to paſs over the diſk of jupiter in the form of a dark ſpot; but at
another time has been known to paſs over it with its light fo fimilar to that
of jupiter, as not to be diſtinguiſhable from it, by the beſt teleſcopes; except
at its entrance and exit. To account for this, we muſt ſay that, either the
fpots are fubject to change, as thoſe of the fun and fome of the primary pla-
nets are found to be; or, if the fpots be permanent, like thofe of the moon,
that the fatellits, at different times, turn differe parts of their globes towards
us: it is probable both thefe caufes contribut to produce theſe appearences:
they turn round their own axes; and the fpots are variablea. From the
ſame cauſes, both the light and apparent magnitude of the fame fatellit is vari-
able: for, the fewer ſpots there are upon that fide of it which is viſible to
us, the brighter will it appear: and, fince only the bright part is viſible, a
fatellit muſt appear larger, the more of its bright fide is towards cur earth;
leſs, the more it happens to be covered with ſpots on that fide of it which
is expoſed to our view. The fourth, that is generally the leaft, is fome times
bigger than any of the reft: the third uſually appears the largeſt; but fome
times feems the leaſt of them: in ſhort, they are all variable, both in bright-
neſs and apparent magnitude. A fatellit may be fo covered with ſpots, as
to appear leſs, when detached from jupiter than the ſhadow thereof upon
his difk: though we are fure, by § 982, the ſhadow is leſs than the body
that cafts it. To a fpectator placed upon jupiter every fatellit would ap-
pear to go through all the phaſes of the moon § 971: but to the inhabitants of
the earth they turn the illuminated half of their globes very nearly in the fame
manner as jupiter was faid to do, § 726, and 972.
74
·
1106 Every fatellit, in going through its inferior femicircle, may caft a fha-
dow upon its primary, while it is paffing between the fun and its primary; this
would cauſe an eclipſe of the fun, to a ſpectator placed upon that part of jupiter
over which the ſhadow of the fatellit paffes: the paffage of the fhadow over the
diſk of jupiter may, in ſome fituations of the earth with refpect to jupiter
and the fun, be feen by us with good teleſcopes; either going before or fol-
lowing the fatellit: in fig. 74, let ABCD be the orbit of the earth, EF part
of the orbit of jupiter, defgh the orbit of a fatellit, wherein it moves ac-
a Memoires d'Acad. 1707 & 1724.
1
cording
CH A P. 7.
453
ASTRONOMY
cording to the order of the letters: when the fatellit is at d, the ſhadow of FIG.
it upon jupiters difk is at b; if the earth be then at A, the fatellit will appear 74
at a, eastward from the fhadow: in this cafe, as the apparent motion of
both is in the line abc from a to c, the fatellit appears to follow the ſhadow:
but, if the earth be then at c, the fatellit will appear at c, and, in that caſe,
muſt be ſeen to go before the fhadow. In the figure before us, when the
earth is at D, jupiter is in conjunction with the fun: when at B, in oppofition:
fo that, from conjunction to oppofition, while the earth is going in the ſe-
micircle D C B a fatellit follows the fhadow; from oppofition to conjunction,
while the earth is going in B A D the ſhadow follows the fatellit.
1107 Every fatellit, in going through its fuperior femicircle, may paſs
through the ſhadow of jupiter, or fuffer an eclipse, in the fame manner as
the moon does in paffing through the fhadow of the earth: this is always
the caſe of the three innermoſt ſatellits; the fourth, by reaſon of the larg-
nefs of its orbit, will, when near either limit, not be eclipſed, nor ſuffer
any occultation; for it will not be hid behind the body of jupiter, nor paſs
over his diſk, nor go through his fhadow, but will be carried either above
them, more northward, or below them, more towards the fouth. The be-
ginnings and endings of theſe eclipfes are eaſily ſeen with the teleſcope,
when the earth is in a proper fituation in refpect of jupiter and the fun:
the entrance of a fatellit into the fhadow fo as to diſappear we call its im-
merfion: the first appearance of it on coming out of the fhadow is called its
emerfion. Though the shape of jupiters ſhadow upon a fatellit cannot
be ſeen by the beſt teleſcopes, no doubt, it is circular, as we find the ſha-
dow of the earth to be in a lunar eclipſe.
1108 When jupiter is in conjunction with the fun, or near it, the fuperior
brightneſs of that great luminary renders the planet as well as its fatellits
invifible. From the time of jupiters first appearing after conjunction
till near his oppofition, the immerfions only of the fatellits are viſible:
when jupiter is in oppofition, only their occultations can be obſerved, by
their going behind, or paffing over the difk of the planet: from the oppo-
ſition to near his conjunction, the emerfions only are to be feen. Thus, fig.
74, if the earth be at A, the entrance of the fatellit into the fhadow at f 74
may be obſerved, but its emerfion at g cannot be ſeen; becauſe the body of
jupiter comes between the eye of the ſpectator and the point g: on the other
hand, if the earth be at c, the emerfion of the fatellit at g is vifible; but its
immerfion at ƒ is not fo; becauſe the point ƒ is hid from the eye by the
body of jupiter. What is here faid is exactly true as to the first fatellit, where-
of an immerſion with its immediately fubfequent emerfion can never be ſeen
by
3 M
454
BOOK 3
ASTRONOMY
FIG. by us and it is but rarely that they are both viſible in the fecond; for in
order to their being fo, that fatellit muſt be near one of its limits at the ſame
time that jupiter is near both his perihelion and his quadrature with the fun:
as to the third fatellit when jupiter is more than 46 degrees from
conjunction with or oppofition to the fun, both its immerfions and inmedi-
ately ſubſequent emerfions are vifible, as they are alfo in the fourth when
the diſtance of jupiter from conjunction or oppofition is 24 degrees: thus,
74 fig. 74, let N o be part of the orbit of the third or fourth fatellit, when the
earth is at or near A or c, the immerfion at L and emerfion at м are both
vifible to us.
When jupiter is in quadrature with the fun, the earth is fartheft out of
the line that paffes through the centers of the fun and jupiter; and therefore
the ſhadow of jupiter is then moſt expoſed to our view: but even then
the body of the planet will hide from us one fide of that part of the ſhadow
that is very near it, through which the first fatellit paffes; and this is the
cauſe that, though we may fee either the entrance of that fatellit into the
ſhadow, or its going out therefrom, according as the earth is fituated on
the weft or the eaft fide of the fhadow; we cannot fee them both: whereas
the other fatellits going through the ſhadow at a greater diſtance from jupiter,
their ingreſs into it and immediately ſubſequent egrefs out of the fame may
both be ſeen, when jupiter is in or near his quadrature.
1109 The duration of an eclipfe is longeſt when a fatellit is in one of its
nodes; for then it deſcribes a diameter of the circle of the ſhadowa: in every
other fituation a fatellit paffes over a chord of that circle: the farther the ſa-
tellit is from its nodes the lefs is the chord, and the ſhorter the duration of
the eclipfe: the fourth fatellit, when above 52 degrees from its nodes, by
reaſon of its diſtance from jupiter, always eſcapes being eclipſed.
The duration of the eclipſes of the ſecond and third ſatellits near their li-
mits is much longer at one time than at anotherb: this fhews the inclinations
of their orbits to be variable; for the ſhadow of jupiter is fo nearly cylindri-
cal that a ſmall excentricity in the orbit of a fatellit, which carried it
through the ſhadow a little nearer to the body of jupiter at one time than at
another, would not cauſe a fenfible difference in the duration of eclipfes:
and the utmoſt elongation of each fatellit being always the fame, fhews
plainly that none of them have any confiderable excentricity.
1110 No excentricity hath been hitherto diſcovered in the orbit of the
firſt fatellit; the inclination of its orbit to the orbit of jupiter was ſettled
Domenico Caffini in the laft century at 2° 55', and the afcending node of it
a See what was faid of the circle of the earths fhadow § 993.
b Mem. d'Acad 1729, 1734.
about
CHAP. 7.
455
ASTRONOMY
about the middle of; and there does not appear any reafon to make any
change in either of thefe. The Jecond is not yet known to be elliptical,
though fufpected to be foa.
CC
>
"Mr. Dunthorne, who has compared together a very great number of ob-
"ſervations, communicated to me the following particulars, as the reſult of
"that compariſon; that the aſcending node of the fecond fatellit ſeems to be
"about the 5° of, and to be at reft: that the inclination of its orbit va-
"ries from 2° 50 to 3° 52′, was leaſt in 1668, greateſt in 1715; and feems
to have made one revolution and an half during the intermediate years.
"That the orbit of the third hath a very ſmall excentricity, ſcarce ſo much
'as a third part of the excentricity of venus: that its apojovium in 1728
"was near the 10th degree of r, and moves forward about three figns in
50 years: that, in the year 1727, the aſcending node was in 16° of
"and moves forward about 8º in 60 years: that the angle of the inclination
"of its orbit to that of jupiter, in the year 1695, was 3°, and has been in-
creafing ever fince; and ſeems as if it would get to its maximum about the
year 1765, and would be then about 3° 24. That the orbit of the fourth
fatellit is a little more excentric than that of venus: that, in the year
1728, its apojovium was in 12° 30′ of x, and moves forward about 2 figns
"in 100 years: that, in 1730, the afcending node was in 13 or 14° of ≈≈,
"very near the place where Domenico Caffini had found it 60 years before:
"that the inclination of its orbit is about 2° 40', and does not feem to vary
"above one or two minutes either way."
<<
1111 The periodical times of the fatellits have been given already § 1999;
but they are fubject to fome inequalities which require equations; that is,
ſome minutes muſt be added to or taken from the times of their conjunctions
with jupiter according to their mean motions, if we would have the true times,
in order to predict their eclipfes: one inequality is owing to the mutual
gravitation of the fatellits towards each other, and has its period of about
437 days: in that time the three innermoft fatellits return into the fame fi-
tuation in reſpect of one another: this irregularity is fmall in the firft,
ſmaller in the third, not perceptible in the fourth, but very confiderable in
the ſecond fatellit; fo that, without this equation, it may fome times deviate
from its place by calculation 10, 20, 30, or even 40 minutes in time b.
"Mr. Dunthorne, makes the greateſt deviation to be 34 minutes."
1112 Another inequality arifes from theſe two cauſes, that the progress of
light is not instantaneous, but, though inconceivably ſwift, takes fome time in
a Bradley in notis ad tabb. fas.
b Bradley, ibid.
3 M 2
paffing
456
воок 3.
ASTRONOMY
8
FIG' paffing from one place to another; and that the earth varies her diſtance
from jupiter, by going round her annual orbit: thus, immerfions more and
more anticipate their times by calculation, as the earth approaches to jupi-
ter; and emerfions appear later and later after their times by the tables,
74 when the earth is going farther off from jupiter: in fig. 74, while the earth
is going from D to A, from A to B, ſhe is approaching nearer to jupiter, at
A ſhe is nearer to him than at D by the line AG equal to s D a femidiameter
of the orbit of the earth; and an immerſion that happens then will appear
minutes fooner, and when the earth is come near to в fhe will be a whole
diameter of her orbit B D nearer to jupiter then ſhe was at D; and an immer-
fion that happens then will appear 16 minutes fooner than it would have
done had the earth continued at D: on the other hand, in the femicircle B
CD the earth is receding from jupiter; and, an emerfion when the earth
is come to c will be feen about 8 minutes later, and when the earth is
advanced to D 16 minutes later than if the earth had ftaid at B: to make
this more eafily apprehended, we may confider the firſt ray of light from
the fatellit that reaches our eye upon its coming out of the ſhadow as a
meffenger, that brings us word of its emerfion; and the laſt ray of light
which comes from it before it goes into the fhadow as one that gives no-
tice of its immerfion. If a perſon were to travel with news from London
northward, at the even rate of 5 miles an hour, if I ſtaid at Cambridge, I
ſhould receive any meffage that he brought in 10 hours after his ſetting
out; if I went 5 miles towards London, I fhould have it in 9 hours: but
if I went 10 miles towards the north of Cambridge, he muſt travel 12
hours before he could reach me. See the velocity of light more accurately
determined from the aberration of the ſtars, § 872.
1113 From the progrefs of light being thus in time, it neceffarily follows
that all the heavenly bodies appear to us not in the places where they are at
the time when we obferve them, but where they were fome time before;
and this interval of time between their being in a place and being feen there-
in is greater, the greater their diſtance is from the earth: thus we obferve
the fun in the meridian, when he has really left it 8 minutes before our
viewing him there; for fo long time does light ſpend in travelling from the
fun to our earth: thus a ftar may appear to us in the zenith, or ſome other
point in the heaven, whereas thoſe rays of light which this moment enter
our eyes and ſhew it us there may, by reaſon of its vaft diftance, have been
emitted from the ſtar ſeveral days, or even weeks before. From hence this
paradox may be verified that, if the ftars were to be this moment extin-
guiſhed, we might continue to ſee them ſome days, or even weeks and
years.
This
CHAP. 7.
457
ASTRONOMY
This has occafioned fome writers upon this fubject to ſay that, in the immenfe
expanſe of ſpace, the diſtance of fome ftars may be fo great, that their light
has not yet had time to reach our earth, though they were created fome
thoufand years ago: as to that, if a ſtar were at ſuch an unmeaſurable diſtance
as is here fuppofed, it muſt be quite invifible to us, even with the beſt te-
leſcopes; for the fame reaſon that a great number of ſmall ſtars are fo to the
eye unaffifted by glaffes.
1114 The beginnings and endings of the eclipfes of jupiters fatellits are in-
ftantaneous; and therefore of great uſe to aſcertain the different longitudes of
different places, fee § 313 and 314: this they do more accurately than eclip-
fes of the moon, fee § 998: the firft fatellit is the moſt proper for this pur-
pofe; by reaſon of the greater velocity of its motion, and the frequency of
its eclipfes in order to be exact in our obfervations, the length of the tele-
ſcope made uſe of and the conftitution of the air fhould be mentioned; for,
though, at an immerſion, a fatellit diſappears in an inſtant, and, at an emer-
fion, comes into view at an inftant, theſe inſtants of time are not preciſely
the fame to different obfervers: at an immerfion, a fatellit in going into the
ſhadow ſeems to grow leſs and lefs, till the bright part is too ſmall to be ſeen
by the teleſcope made uſe of: at an emerfion, a fatellit appears very ſmall at firſt,
as foon as ſo much of it is come out of the ſhadow as is fufficient to make it
vifible by the teleſcope through which it is obſerved; and then grows gradu-
ally larger, till it is quite clear of the ſhadow: the better the teleſcope is the
later is the immerfion, and the fooner is the emerfion obferved; a fmall dif
ference between teleſcopes will not make a fenfible difference in the times of
them, if obſerved in the fame place: whereas, when obſerved in different
places, the air in one place may be fo much clearer than in the other as to
make a fenfible difference in the times; not to mention the difference in the
eyes of different men, by reaſon whereof a very ſmall object ſhall be ſeen
by one which is invifible to another.
1115 Nic. de l'lfle and his brother at Peterſburgh, obferved the fame immerfi-
on of the firſt ſatellit, one with a tube of 15 feet, the other with one of 201;
and through the longeſt teleſcope the immerſion appeared 5 or 6 ſeconds in
time later than by the other: the difference between a tube of
13
feet and
one of 15 they found to be 3 feconds: between a tube of 13 and one of 201
the difference was 10 feconds: and a Newtonian reflecting teleſcope that
magnified above 200 times, fhewed the firſt ſatellit at an immerfion 15 feconds
longer than it could be ſeen by a tube of 13 or 15 feet: other obſervers
found a difference of 5 or 6 feconds between tubes of 20 and 22 feet; which
he
458
BOOK 3
ASTRONOMY
he thought was in part owing to the difference in their eyes.
Acad. Petropolitan. vol. 1. ann. 1726.
Commentar.
In another place, he tells us the firft fatellit, before an immerfion, or rather
before an occultation, feemed to adhere for ſeveral ſeconds to the edge of
jupiters difk: what I tranflate feconds is in the original minuta; but I
think it ſhould be read minuta fecunda. That the difference of the air will
cauſe a difference in the times of immerfions or emerfions is certain, from
what Maraldi obſerves, that the difference in longitude between Greenwich
and the obfervatory at Paris comes out greater from immerfions than from
emerfions of the first fatellit; this he thinks is owing to the air being
clearer in the environs of Paris than thoſe of London.
Caffini found a difference of 30 ſeconds between the times of the fame
immerfion of the firft fatellit obferved with a teleſcope of 10 feet and one of
16; and this was propoſed for a rule, whereby to eſtimate what allowance
ſhould be made for teleſcopes of a different focal length: Hift. d'Acad. 1729.
But teleſcopes of the fame length may be of different goodneſs, ſo that one
will ſhew an object that cannot be ſeen by another: there muſt therefore
be fome little uncertainty in this affair, what ever caution we take; the
beft way of coming as near the truth as poffible in aftronomical matters is
by a number of obſervations, in order to take a mean between the greateſt
and leaſt numbers.
1116 If the time of an immerfion or emerfion be calculated for the me-
ridian of any place, the difference in time when the fame is obferved in ſome
other place turned into degrees minutes and ſeconds by § 316, gives the dif-
ference in longitude between thoſe two places: thus, if an immerſion, by the
the tables, falls out at 12 at night at Greenwich, and the fame be obſerved
at fome other place the longitude whereof is unknown, at 30 minutes after
ten at night, that place is diftant from Greenwich in longitude 22° 30′
weftward.
The longitude of many places upon the earth has been fettled, fometimes
by the tables in the way juſt now mentioned; but generally by the more
exact method of obfervations actually made in different places: and this is
the uſe of obſerving continually as often as opportunity ſerves immerſions and
emerfions of the ſatellits of jupiter, eſpecially the firft, at the great obſerva-
tories in various parts of Europe, as Greenwich, Paris, Peterſburgh, &c.
the longitudes whereof are known; and publiſhing from time to time collec-
tions of fuch obfervations: thus, for example, if a perfon has noted down
the time of an immerfion at the Cape of Good Hope, and, upon his return
་
to
CHAP. 7.
459
ASTRONOMY
to Europe, finds the time of the fame immerfion in a collection of obferva-
tions made at Greenwich, he may know the difference between the longi-
tude of the Cape and that of Greenwich.
1117 I have mentioned before, § 1114, fome difficulties in fettling the
exact time of eclipfes or occultations of the fatellits; I fhall only add that
long teleſcopes are beft, but if they be expoſed to a ſtrong wind the obſer-
vation will be uncertain: that the twilight or bright moon light, as they ren-
der ſmall ſtars inviſible, will alſo prevent the fatellits of jupiter being ſeen
ſo ſoon at an emerfion, or fo late at an immerfion, as they would be in a
dark uncloudy night: yet, notwithſtanding all the little errors to which the
obſervations of theſe appearances are liable, they furniſh us with the beſt
method hitherto known of determining the longitudes of places upon
upon earth;
on which account they are well worth all the pains it hath coſt aſtronomers,
and thoſe pains have been more than a little, in their endeavours to bring
the tables of the motions of the fatellits of jupiter, efpecially of the firſt,
to the utmoſt perfection of which they are capable.
By this method, geography has received great improvement, and is every
day advancing to greater perfection; great errors in our maps are correct-
ed; for inſtance, the moſt remote places in the eaft and weft Indies were
found to be 25 or 30 degrees nearer to us than they were before thought to
be; the Cape of Good Hope to be 7 or 8 degrees more wefterly than it was
laid down in the maps. Du Hamel, Hift. Reg. Acad. 1. 2. c. 3. v. Phil,
transact. n. 183.
The French aftronomers have, by this method, and that mentioned § 416,
made a correct map of France: it would certainly be well worth the while
to have the like done for Great Britain, at the expence of the public; eſpe-
cially to have the coafts carefully laid down: and not only the coafts of our
own iſland, but of all thoſe parts of the world to which we frequently fail:
this would render navigation much more fafe and certain than it is at pre-
fent, and preſerve many lives that are now loft: and indeed if the coafts at land
are not well determined, it is of little ufe to be able to find the longitude
at fea: thus, for inftance, if I were bound to Barbadoes, it would not
be of any ſervice to know at fea my diftance from London, if I knew
nothing of the fituation of Barbadoes.
1118 As to finding the longitude at fea by the fatellits of jupiter, they may
be ſeen very well with a teleſcope of 6 or 8 feet, and, when the fea is calm,
their immerſions and emerfions may be obſerved aboard a ſhip under ſailª:
perhaps fome perfons, by frequent practice, might arrive at a facility in doing
a Obfero, par M. de la Condamine, Mem. d'Acad. 1732.
it,
460
воок 3.
ASTRONOMY
it, as we find fome come to a dexterity in ſhooting flying that others never
can attain: what ever ufe can be made of obfervations of the fatellits at fea
with tables of their motions, muft be liable to the errors of thoſe tables; as
well as to errors in taking the height of ftars, to determine the time of night
in the fhip where they are obſerved, in order to compare it with the time
in the place for which the tables were calculated: the time of night at fea
is found by the latitude, and the height of a ſtar the right afcenfion and de-
clination of which is known, § 788: the latitude is found by § 568: the
height of a ſtar by § 283 286, in this method, tables calculated, fup-
poſe for Greenwich, are inſtead of another obferver at Greenwich; the tables
are not yet brought to fuch perfection as to be depended upon equally with an
actual obfervation; but they have this conveniency that they may be confult-
ed immediately before or after the obfervation at fea, whereas an account
of the actual obfervation. at Greenwich could not be had there, time enough
to be of any uſe: they are alſo uſeful and neceffary to inform us when to
look for immersions or emerfions.
•
1119 If a clock aboard a ſhip fet to the time of day at a place from which
the ſhip is departing, fuppofe London, could be made to keep equal time
without any variation, it would continually fhew the time of day at London,
in what place foever the fhip were; and then, in order to find the lon-
gitude at fea nothing more would be requifite, but to find the time of day
or night aboard the ſhip, by the fun or ſtars, § 788: for the difference be-
tween the time fo found and the time by the clock, in hours minutes and
feconds, turned into degrees minutes and feconds, would fhew the longitude
from London. § 312, 313, 316, 317. The common clocks are ſubject
to fo great irregularities from change of weather, heat and cold, drynefs
and moisture, befides the rolling of the ſhip, that they cannot be depend-
ed upon at all, in a long voyage, to keep the time they fet out with: I have
fometimes thought that feveral clocks and watches made of different ma-
terials and upon different principles might correct one another, fo that the
mean between the exceſs and defects of them all might be the time required:
but there is a clock and watch of a new conſtruction invented by Mr. Harrison
now upon tryal, that is thought to promiſe fair for keeping time at fea, in
all weather and in all climates.
1120 If a clock, the motion whereof is regulated by a pendulum, be made
to keep equal time ever fo well, aboard a fhip, it will do fo only while the
ſhip continues in the fame latitude; for, if it be carried nearer to the
equator,
it will go flower, if toward the poles it will go fafter; fo that, in the firſt
caſe the pendulum muſt be lengthened, in the fecond cafe it muſt be ſhort-
ened,
CH A P. 7.
461
ASTRONOMY
ened, to make the clock keep time, § 448. v. Neuton. princip. pag. 384.
edit. 2. Cantab. 1713. No mechaniſm can be contrived to prevent this
inconvenience, during a voyage at fea: the only remedy for it muſt be,
by a calculation, to find what allowance is to be made for the change
of latitude; and this I think is impracticable, except that change were made
regularly, which never is the cafe: in a fhort voyage, or where there is
not great change in the latitude, a clock that kept time would be of very
great fervice to find the longitude at fea. The oftener there are opportuni-
ties of going a fhore at places the longitude whereof is known, in order to
correct the clock, the better. If a watch could be made to keep true
time at ſea, it would not be liable to this defect.
An error of one minute in the time, whether taken from a clock or found
by any celeſtial obfervation, will, under the equator, cauſe an error in the
longitude of 15 geographical miles, § 316; in our latitude of 52 degrees, the
error will be about 9 miles, § 484: an error of 20" in time would cauſe,
under the equator, an error in the longitude of 5 miles; in our latitude,
of about 3 miles: and fo on in that proportion for ſmaller errors in the time.
1121 In order to determin the real magnitudes of the fatellits, their appa-
rent diameters have been compared with the apparent diameter of jupiter,
by obſerving the time a fatellit takes between its firſt appearing to touch
the edge of that planets diſk and its being totally entered thereon; or the
time between its coming to touch the fartheft edge and going entirely off
from the diſk, and comparing one of theſe intervals with the time the cen-
ter of the fatellit ſpends in paffing over the middle of the difk: this obfer-
vation is liable to uncertainty; by reaſon of the ſpots which vary the appa-
rent diameters of the fatellits, and is otherwiſe fo difficult to make, that
Maraldi owns he attempted it without fuccefs; but gives us ſome obſervati-
ons of this fort made by Dom. Caffini, by which it appears that, in coming
on or going off the difk, the first and fecond fatellit took up each a
twentieth part, the third fatellit about an eighteenth part of the time that
they reſpectively ſpent in croffing over the diſk near the center; as to the
fourth, Maraldi concludes from the tables it is about 15 minutes in going on,
and 5 hours in croffing the difk: this fhews the diameter of the third fa-
tellit is to the diameter of jupiter as 1 is to 18; the diameter of each
of the other three as I to 20: the fame Caffini, finding the apparent dia-
meter of jupiter in his perihelion 50°, from that, and his diſtance from
the fun compared with our earths diftance, computes the diameter of
jupiter to be 10 of the diameters of the earth: this brings out the real
3 N
diameter
......
462
BOOK 3
ASTRONOMY
diameter of a fatellit about half the diameter of the earth: the third is a
little bigger than any of the reſt. Mem. d'Acad. 1734. The apparent dia-
meters of the fatellits are meaſured by this method with greateſt exactneſs
when they are largeſt: for, as the bright part only is vifible, a fatellit is ſeen
in its true dimenfions when clear of fpots; and will appear to be longer in ma-
king its entrance upon the diſk of jupiter and its exit therefrom, than when the
fide turned towards us hath ſpots upon it: thus, the ſame fatellit which at one
time ſpends to in its entrance or exit, at another time takes no more than
6' in the fame: the fourth fatellit was once obferved to take up but half the
uſual time in making its exit: this was thought to be owing to its having
a ſpot upon it that covered half its diameter. Mem. d'Acad. 1734. All the
fatellits appear lefs when near jupiter: their light is enfeebled by his fuperi-
or luftre, as that of the ſtars is by the nearness of the moon.
Caffini fufpected the firſt ſatellit to have an atmoſphere; becauſe the ſha-
dow of it could not be feen, when he was fure it ſhould have been upon the
diſk of jupiter, if it had not been ſhortened by its atmoſphere, as is the caſe
of the fhadow of our earth, § 983. Du Hamel, Hift. 1. 2. c. 1.
Remarks upon CHAP. 7.
1122 The elements of the eclipſes of the fatellits of jupiter, or things ne-
ceffary to be known in order to conſtruct tables of them are thefe; 1, the times of
their revolutions round jupiter: 2, the time of jupiters revolution round the
fun: 3, the time of the earths annual revolution: 4, the diameter of jupi-
ter and of his ſhadow: 5, the diameters of the orbits of the fatellits: 6, the
places of the fatellits nodes: 7, the inclination of their orbits to the orbit
of jupiter: the firſt of theſe, the periodical times or mean motions of the
fatellits are found by their conjunctions with jupiter; thus, if two conjuncti-
ons of a fatellit with the center of jupiter confiderably diftant in time be
obſerved, and the interval between them divided by the number of the
intermediate revolutions, the quotient will be the time of one revolution:
the moment of the conjunction of a fatellit is the middle of its eclipſe, or
occultation: the midde of an eclipfe or occultation is found by obſerving
the moments of the beginning and ending thereof: the conjunction of the
fourth fatellit, when it neither fuffers an eclipfe nor occultation, but paffes
north or fcuth from both the difk and ſhadow of jupiter, may be obſerved
immediately, by the cross hairs in a teleſcope.
Scholium, in all theſe obſervations, the motion of the earth and of jupiter
during the intermediate time muſt be taken into the account.
1123
page 463
Book III.
N
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83
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A
81
85
87
89
FA
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B
82
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་་་་་་་
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86
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་་་་་
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84
86
88
90
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CH
UNIV
Σ
CHAP. 7.
463
ASTRONOMY
1123 The revolutions of the earth and jupiter are known by § 915: the di- FIG.
ameter of the orbit of a fatellit is found by taking the diſtance of it from the
center of jupiter, at its utmoſt elongation, with the micrometer: when the
diameter of the orbit of one of the fatellits is known, the diameters of the reſt
are found by this analogy, the ſquares of their periodical times are as the cubes
of their diſtances from their primary: ſee § 90 and 914. Other methods may
be ſeen in Caffini, elements d'aftronomie 1. 9. c. 3. The real diſtance of
the firſt fatellit from jupiter is computed to be nearly equal to the diſtance
of the moon from our eartha: the apparent diameter of jupiter is given
§ 908 and 1121: the diameter of the fhadow differs not fenfibly from that
of the planet; efpecially in the place where the first fatellit paffes through
it: the nodes of a fatellit are found by thoſe eclipſes or occultations that are
of the longeſt duration, for then the fatellit paffes through a diameter of the
fhadow, or of the difk: the inclination of the orbit of a fatellit is diſco-
vered by an eclipfe or occultation of the ſhorteſt duration, compared with
one of the longeft; for, as the time of the longeft eclipfe is to the time
of the ſhorteſt, ſo is the diameter of the fhadow of jupiter to the chord
thereof deſcribed by the fatellit, in the ſhorteſt eclipſe; from whence the
diſtance of the chord from the center of the ſhadow, or the inclination may
be found. v. Caffini ibid. When the fourth fatellit, in its conjunction, eſcapes
both the ſhadow and diſk of jupiter, the diſtance of it from the center of jupi-
be meaſured by the micrometer; and the angle of inclination found.
1124 In the five following figures, I have given perſpective views of ju-
piter and the circle of his ſhadow and part of the orbit of a ſatellit, as they
would appear to us if viſible: the circle of the ſhadow is no otherwiſe viſible
to us than by its effect, making the fatellit to diſappear all the while it is
paffing through it. Fig. 75 and 76, repreſent a ſatellit going into the fha- 75
dow at a, and coming out of it at b: here both entrance and exit are vifible; 76
and the duration of the eclipſe may be obſerved directly. Fig. 77 exhibits 77
jupiter with part of his fſhadow on the weft fide of him, the reſt being hid
by the interpofition of his body; in this cafe, only the entrance of the fa-
tellit at a can be ſeen. Fig. 78 fhews jupiter with part of his ſhadow on the 78
eaſt fide; here only the exit of the fatellit at b is vifible. Fig. 79 is a view 79
of jupiter and the entire orbit of the fourth fatellit, in a fituation wherein it
neither falls into the fhadow: nor paffes over the difk of jupiter: fig. 80 80
fhews the fame fatellit paffing through the edge of the fhadow, and fuffer-
ing a partial eclipfe, as obferved by J. Caffini mem. 1712.
ter may
a Cafini, Mɛmoïres d'Acad. R. annec`17 16.
3 N 2.
CHAP.
464
BOOK 3.
ASTRONOMY
FIG.
CHAP. 8. THE RING OF SATURN: HIS MOONS OR SATELLITS.
1125 Saturn is furrounded with a broad thin ring, the edge of which re-
flects little or none of the funs light to us; the planes of the ring reflect the
light of the fun in the fame manner as the planet does: if we fuppofe the
diameter of faturn to be divided into 3 equal parts, the diameter of the ring
is about 7 of thoſe parts: the ring is detached from the body of faturn in
fuch a manner that the diſtance between the innermoft edge of the ring and
the body is equal to the breadth of the ring. Whifton in his memoirs of the
of the life of Dr. Clark, relates the Doctors Father to have ſeen a ftar through
that ſpace between the planet and the ring; and thought he was the only
perſon who had ever happened to ſee a fight that muſt be very rare; for
that opening, though in reality of very large dimenfions, by reafon of its
great diſtance, appears extreamly fmall to us.
1126 Galileo was the firft who diſcovered any thing uncommon in ſaturn:
through his teleſcope he thought he faw that planet appear like two finaller
globes on each fide of a large one: in the year 1610, he gave out his diſco-
very in a latin fentence, the meaning whereof was that he had feen faturn
appear with three bodies; but the letters of the fentence were tranfpofed,
to keep his diſcoveries fecret for ſome time, leaft fome other perſon ſhould
pretend to the fame. After viewing faturn in this form for two years, he
was ſurpriſed to ſee him become quite round, without his adjoyning globes,
for fome time, and after that appear again in his triple form, as before: and
now faturn was obſerved by feveral other aftronomers, fome of whom, for
want of good glaffes, or of fkill in drawing what they faw, publiſhed figures
not very like what he appears through a good teleſcope.
1127 About 40 years after Galileo, Hugens, having greatly improved
the art of grinding object-glaffes, firft with a teleſcope of 12, and afterwards
with one of 23 feet that magnified the object an 100 times, (whereas that of
Galileo magnified but about 30 times,) diſcovered the true ſhape of faturns
ring; and in 1659, publiſhed his fyftema faturnium, wherein he explains all
the appearances thereof, in a method that is now generally thought fatif-
factory: from that treatiſe, and from what is to be met with in the philo-
fophical tranſactions, and the memoirs of the royal academy, what here
follows of the aftronomy of faturn is chiefly compiled.
1128 If we had a view of faturn and his ring with our eye perpendicular to
81 one of the planes of the ring, we fhould fee them as in fig. 81; but our eye
is never elevated ſo much above either plane as to have the viſual ray ftand
at
CHAP. 8.
465
ASTRONOMY
'
at right angles to it: our eye indeed is never elevated more than about 30
degrees above the plane of the ring: for the moſt part we view the ring
at an oblique angle, fo that it appears of an oval form, the outward cir-
cular rim is projected into an ellipfis, as is alſo the inner rim, more or leſs
oblong according to the different degrees of obliquity with which it is
viewed, § 285: fometimes our eye is in the plane of the ring produced,
and then faturn appears round: the ring is then invifible, either becauſe
the outward edge is not fitted to reflect the funs light towards us, as
Hugens thought; or becauſe it is ſo thin as to be too ſmall an object to be
feen by us at fo great a diſtance, as was Dr. Jurin's opinion. See his effay
upon diſtinct and indiſtinct viſion at the end of Smith's optics p. 154.
1129 The plane of faturns ring in every part of his orbit, is parallel to
it felf in every other part of his orbit. The plane of faturns ring makes an
angle with the plane of his orbit of 31°. The plane of faturns ring produ-
ced to the ſphere of the fixt ſtars, cuts his heliocentric orbit in two oppofite
points, which are called the nodes of the ring. The places of the nodes are
about 20° of and . It cuts the ecliptic alfo in two oppofite points, at
its inclination to the ecliptic is 31° 20. Maraldi
16° 4′ of " and
Mem. d'Acad. 1715.
1130 As faturn paffes from the afcending to the deſcending node of his
ring, the northern fide of the rings plane is turned towards the fun, as he
paffes from the deſcending to the aſcending node of his ring, the ſouthern
fide of his rings plane is towards the fun. To make faturns ring viſible to
us, the fun and our eye muſt be both ſufficiently elevated above the fame fide
of the rings plane; the fun to enlighten the ring, and our eye to receive the
light reflected from it. When faturns heliocentric place is in either of the
nodes of his ring, the plane of it produced paffes through the fun: when he
is within 33′ 30″ of a node of his ring, the fun is not fufficiently elevated
above the plane of it: in both thefe cafes the ring, not being illuminated, is
invifible, though our eye be fufficiently elevated above its plane. When
faturns heliocentric place is near either of the rings nodes, though more dif-
tant from it than 33′ 30″, if our eye be either, 1. in the plane of the ring
produced, or, 2. elevated above the dark fide of the rings plane, or, 3. tou
little elevated above the enlightened fide of the rings plane to have the rays
of the fun reflected to us in a fufficient quantity to make the ring vifible, in
all theſe caſes ſaturn appears round. In every other part of his orbit, the
ring will appear to us an ellipfis, the ſhorteſt diameter whereof will be long-
er, the farther faturn is from the nodes of his ring. Hugen. Syftem. Saturn.
Whiſton, aftron. lect. 19. Greg. aftron. p. 392. Phil. tranf, abr. v. I.
P. 365.
1131
466
воок 3.
ASTRONOMY
FIG.
83
1131 Since the heliocentric motion of faturn is about 1° in a month, and
the limits within which his ring difappears for want of the funs light are
1°ý i. e. 33′ 30″ on each fide of either of its nodes; faturns round phaſe
would continue above a month, though our eye were all the while fuffi-
ciently elevated above the plane of the ring. Since faturn may be ſtationary,
and retrograde, if feen from the earth he be coming to one of the nodes of
the ring near the end of his direct motion, his round phaſe may laſt about 9
months and that fometimes without interruption. Maraldi, mem. an. 1715.
1132 When faturn appears round, if our eye be in the plane of the ring
produced, the edge of the ring will appear as a dark line, crofs the center
of the planet: if our eye be elevated above the plane of the ring, there will
be vifible croſs the middle of the difk a fhadowy belt, caufed, 1. by the fha-
dow of the ring, 2. by part of the ring, which is then obfcure, coming be-
tween our eye and the planet. The rings fhadow is broadeft, when the fun
is moſt elevated, the obfcure parts of the ring appear broadeft, when our
eye is moſt elevated above the plane of the ring. Saturns ring ſeen through a
very long teleſcope feems to be divided into two concentric rings: that neareſt
his body is the brightest. Caffini ap. Lowth. Tranf. Vol. I. p. 367. Pound, ap.
Jones Phil. Tranf. abr. v. IV. p. 322. Hadley Phil. Tranf. ann. 1723. n. 276.
1133
When faturns ring appears an ellipfis, the parts about the ends of
the longeſt axis reaching beyond the diſk of the planet are called the anfaa.
The anja, a little before and after the rings diſappearing, are unequal in
magnitude: the largeſt anfa is longer vifible, before the planets round phaſe,
and appears again ſooner after it than the other. A. D. 1714. oct. the 1. the
largeſt anſa was on the eaft fide: oct. the 12. the largeſt anfa was on the
weft fide of faturns difk: this makes it probable the ring has a rotation
round the planet. As the ellipfis of the ring, grows narrower, the anſa ap-
pear fhorter; their extremities difappear firft, either becauſe of their narrow-
nefs, or becauſe the outward parts of the ring are lefs bright than the
inward. Maraldi mem. d'Acad. 1715.
1134 The
The 83 figure copied from Hugens, is a perſpective view of the
orbit of the earth, and the orbit of faturn, with the fun in the center of them: at
a, b, c, d, &c. is exhibited faturn, with his ring continually parallel to it ſelf,
during a thirty years revolution through his orbit: at the correfponding capi-
tals A, B, C, D, &c. are ſhewn the various forms under which the ring appears
to us: thus, when faturn is in the afcending node of the ring at a, he ap-
a Anja fignifies an handle, that name was given when teleſcopes were fo imperfect as to repreſent fa-
tuin as a globe with two fmall knobs on each fide: the fame rame is continued, though improper now
the tree ſhape is known.
pears
CHAP. 8.
467
ASTRONOMY
pears round, as at A; the ring being then not viſible: at b the ring appears as FIG.
at B, at c as at C, &c. an ellipfis very narrow at first, with the ends of it
fharp, but growing continually wider, till faturn arrives at ƒ, a quarter of a 83
circle from the aſcending node of the ring; there the ellipfis appears as at F,
the wideft that it ever can be; and from thence grows gradually narrow-
er, and the ends of it or the anfa appear fharper and fharper, all the way
to the deſcending node of the ring at i, where the ring again difappears, and
we again view faturn round, as at 1: from thence, during the other half of
of faturns period, we fee the ring appear as an ellipfis wider and wider, till
he is gotten 90 degrees from the deſcending node, where it is again at the
wideft; and then becomes gradually narrower, till its totally diſappearing
at the aſcending node at a.
1135 It is very eaſy to fee by the figure that, while faturn is going through 83
one half of his orbit, from a through b, c, d, &c. to i, the northern or upper
fide of the ring is illuminated by the fun; but, in going through the other half,
from i through k, l, m, &c. to a, the fouthern or lower plane of the ring re-
ceives his light: it is evident alſo from the figure that, when the ring is in
either of its nodes, the rays of the fun fall upon the edge thereof, and, when
near the nodes, they fall upon one of the planes of the ring with great obli-
quity, and confequently throw very little light thereon; and that, the
farther the ring is from its nodes the ftronger is the light upon it: for it
then falls upon it moſt directly, and therefore faturn then appears brighteſt
to the eye unaffifted with glaffes.
1136 The orbit of the earth is ſo ſmall in compariſon of that of faturn, that
we have at all times nearly the fame view of him, as we ſhould have if we were
at the fun; only, when faturn is near either of the nodes of the ring: the
earth may be ſo fituated, that our eye may be either in the plane of the ring,
or elevated above the dark fide thereof, or too little elevated above the en-
lightened fide of it; in all which cafes we ſhall fee no other part of the ring
except what is between our eye and the body of the planet, and that will
appear thereon as a fhadowy belt, even though the fun fhould fufficiently
enlighten one of the planes to make the anſe viſible to a ſpectator on that
luminary.
1137 The four following figures taken from Hugens, fhew faturn with
his ring in different forms; they are not inverted as they appeared in the te- 84
leſcope of two convex glaffes, but in their true pofition: in fig. 84 the ring
is a very oblong ellipfis, the anfæ narrow, the fhadow of the ring fouth
from or lower than the longeſt axis of the ellipfis; the planet being then
coming from the afcending and got near the defcending node of the ring; in
or
468
BOOK 3
ASTRONOMY
FIG. or near which it was a few days after, and appeared as in fig. 85, the ring
85 being then invifible. In fig. 86, the ring is a narrow ellipfis, being lately
86 paſt the deſcending node, the ſhadow of the ring now north from the long-
eft axis: fig. 87 the ellipfis wider, and fig. 90 at the utmoſt width, the ſha-
88 dow of the ring upon the planet more to the north of the longeſt axis.
89
Fig. 89 is from a drawing I took by an excellent 12 foot teleſcope be-
longing to Pemb. Hall, but having omitted to ſet down the date, I cannot
now tell how many years fince: by the form, it muſt have been while faturn
was going from his afcending towards his defcending node, the fartheft half
of the ring is not fo bright as the neareſt, the different parts of the planet
are a little differently illuminated, I believe I took it as it then appeared to
99 me, when my eyes were much better than at preſent. Fig. 90 is as feen in
Mr. Hadleigh's reflecter, exhibited in the Phil. Tranf. n. 378: that learned
gentleman, upon my aſking him whether the planet and the ring appeared
as diftinct as in the figure engraved, told me, if the paper were placed at the
diſtance of 5 or 6 feet, it would to eyes of the common fort give a very
good reprefentation of what his teleſcope fhewed him.
90
1138 Saturn hath five moons or fatellits, which, continually going round
him according to the order of the figns, accompany him in his thirty years
revolution round the fun: their periodical times and diſtances from the cen-
ter of faturn are as followeth,
periodical times.
fatel.
diſtance in femidi-
ameters of the ring.
123
D. H. M. S.
I 21 18
18
2 17 41 22
27
2,097
2, 686
4 12 25 12
4
15
22 41 12
5 79
7 47
47 00
3,752
8,698
in femidia. of the
globe of faturn.
4,893
6,268
8,754
20, 295
25, 348
59, 154
1139 The diſtance of the fourth commonly called the Hugenian fatellit was
accurately meaſured by Pound, with a micrometer fitted to the teleſcope
of above 120 feet, given by Hugens to the royal fociety, and, from the
period and diſtance of that, the diſtances of the reft were computed as above.
Phil. tranf. abr. vol. IV. p. 329. Smiths optics vol. II. p. 444. Halley de
tabulis fatellit. faturn. Caffini elem. d'aftronomie 1. 9. c. 7 & 8.
1140 The orbits of all faturns fatellits, except the fifth, are nearly in
the fame plane, which makes an angle with the plane of faturns orbit of
about
1
87
Book III.
page 469.
92
91
Edip
Edip-
e
e
94
де
k
m
n
96
9
9
98
93
'D.
d
A
C
ň
95
tic
97
tic
M
CHA P. 8.
469
ASTRONOMY
about 31°. They coincide with the plane of faturns ring extended every
way, and therefore the fatellits appear to move in ellipfes fimilar to the el-.
lipfis of the ring; or in ftrait lines, when the ring, if viſible, would appear
as a ſtrait line, by reaſon of its plane extended paffing through the eye of a
fpectator upon the eartha. The orbit of faturns fifth fatellit makes an angle
with the orbit of its primary of 13° 8. Mem. d'Acad. ann. 1717. The lon-
gitude of the aſcending nodes of all faturns fatellits, except the fifth, was
A. D. 1714, determined by J. Caffini to be in 20° 26′ of " the longitude
of the afcending node of faturns fifth fatellit to be in 3° 20′ of . Mem.
d'Acad. 1717 The orbit of the fourth fatellit is excentric; the line of its
apfides and greateſt equation are determined by Halley. Jones, Phil. trans.
abr. vol. I. p. 371.
1141 Many particulars obfervable in the fatellits of jupiter, as their appear-
ing to move in ftrait lines or elliptic curves, to be direct, ſtationary, and
retrograde, &c. are applicable to the fatellits of ſaturn, and therefore need
not be repeated: there is alſo the fame analogy as to their periodical times
and diſtances mentioned § 1123: that the fquares of their periodical times
are as the cubes of their diſtances.
1142 The fatellits of faturn have their orbits inclined to the orbit of
their primary in ſo great angles, that they cannot paſs croſs their primary,
or behind it, or through the ſhadow, except when near their nodes; and
therefore they muſt very rarely ſuffer eclipſes, or occultations. In Phil. tranſ.
abr. v. 4. p. 321. an occultation of the fourth behind the body of faturn, is
related from Mem. d'Acad. R. 1715. There is a curious obſervation of D.
Caffini, mentioned in the Memoires of the R. Acad. of the year 1692, of a
fixt ftar being covered by the fourth fatellit of faturn, ſo that, for about 13
minutes they appeared as one ſtar.
1143 The fatellits of faturn have been diſcovered, as it is natural to fup-
poſe they would be, the largeſt firſt, and the leffer ones afterwards, as tele-
ſcopes were brought to greater degrees of perfection: accordingly, the
fourth which is the largeſt, was firft feen by Hugens, in 1655; who, in 1659,
publiſhed a table of its mean motion: the other four were all diſcovered by
Dom. Cafini, two of them in 1671, the other two neareſt to ſaturn and
the leaſt not till 1686, and that with tubes of 100 and 136 feet; though,
after being better acquainted with them, he could ſee them with a tube of
34 feet. They are not to be feen except the air be very clear. Tables
a Caffini Decouv. de la um. Celefte. n. 25. J. Caffini, Mem. d'Acad. ann. 1714, 1715, 1716, 1717.
Pound ap. Jones Phil, tranf. abr. vol. 4. p. 320. & 329.
30
of
470
BOOK 3
ASTRONOMY'
FIG. of the motions of faturns fatellits, may be ſeen in the Phil. tranf. abr. vol. IV.
in Caffini elements d'aſtronom. vol. II. and in Halley's tables publiſhed 1749.
1144 The fifth fatellit of faturn, or the moſt diſtant one from him is fome-
times in the eaſtern part of its orbit, not viſible; though fought for in a
place where it is known to be, and where at other times it is to be ſeen with
the fame glaffes: this is accounted for, by fuppofing that this fatellit is
fome times covered with ſpots, and at other times free from them; or,
if the fpots upon it be permanent, that it has a rotation round its own
axis. Mem. d'Acad. 1714. Phil. tranf. abr. v. I. p. 368.
1145 Saturn has two belts difcovered by very long teleſcopes, parallel to
the middle belt which is cauſed by the dark edge of the ring when the
planet appears round: thefe belts are rectilinear, when the ring appears
91 elliptic; fig. 91, and confequently, if the ring coincides with the plane of faturns
equator, they are owing to clouds furrounding that planet, at a confiderable
diſtance, and floating in the atmoſphere, which feems to extend beyond the
circumference of the ring. Mem. d'Acad. 1715. J. Caffini, elements d'aftron.
1146 Dom. Caffini fuppofed the ring of faturn might be a great number
of fatellits revolving round him ſo near to that planet and to one another as to
make the interval between them imperceptible, by reaſon of their great diſ-
tance from us: this opinion feems to me fo improbable, that I ſhould not
have thought it worth mentioning, if it had not been advanced by fo great
an aſtronomer: a defire of accounting for appearances the cauſes whereof
are far out of our reach, has often been the parent of hypotheſes not eaſily
to be defended. Mem. d'Acad. 1715.
CHAP. 9. SPOTS IN THE SUN: THE ROTATION OF THE SUN ROUND HIS
OWN AXIS: THE SUNS ATMOSPHERE.
1147 That the fun is fubject to have dark places or ſpots upon his face
was unknown before the invention of teleſcopes; they were firſt obſerved in
the year 1611: whether Galileo at Rome or Scheiner a German jefuit at In-
goldſtadt had the firſt view of them hath been matter of controverfy: but
this is certain that, though Scheiner firft wrote fome letters upon the ſubject,
which were printed in the year 1612 under the feigned name of Apellesa,
a Apelles poft tabulam, alluding to the ſtory told of that celebrated painter, that he uſed to expoſe his pic-
tures to public view, and ftand behind them out of fight, to hear what judgment was paffed on them, by
thofe that went by. v. Erafmi adag. ne futor ultra crepidam.
་
Galileo,
CHAP. 9.
471
ASTRONOMY
Galileo, in the year following, publiſhed a little piece wherein he ſhewed
many miſtakes the then unknown author of the letters had fallen into,
whom however he treated with great civility, and at the fame time gave
ſuch an account of the ſolar ſpots as falls very little ſhort of being all that is
at preſent known of themª. As the uſe of the teleſcope was then pretty well
known, it might eafily happen that theſe two aftronomers, fo far aſunder,
viewed the fun at the fame time, through that inftrument, without one know-
ing what the other had done; however that might be, they afterwards ac-
cuſed one another of plagiariſmb. Scheiner, many years after, in his Rofa
Urfina, a pompous work in folio of four books, employed the firſt book
entirely in clearing himſelf of the afperfion, and retorting it upon his ad-
verfary; and he is by feveral writers of his own order mentioned as firſt
in the diſcovery: but then on the other hand, in a ſubſequent edition of
all Galileo's works, the editors reprinted with them Scheiner's letters, on
purpoſe to expoſe the errors therein, and produced atteftations of feveral
learned men in favour of Galileo's pretentions to priority; in one of which
it is roundly afferted that Scheiner never erected his telefope to view the
fun till after a brother jefuit had informed him that Galileo had diſcovered
fpots upon that luminary d.
Scheiner's Rofa Urfina, though prolix and tedious, has fome merit; for,
having, as he ſays, in his hands above 3000 obfervations made by himſelf
and other mathematicians to whom he had recommended the affair, he pub-
liſhed ſuch as he thought moſt uſeful, corrected the errors he had before
embraced, and fettled pretty exactly the inclination of the axis of the fun to
the ecliptic, and the poſition of his poles. Since that time the ſolar ſpots
have drawn the attention of aftronomers in various parts of Europe; I fhall
here give the refult of their obfervations.
1148 There is great variety in the magnitudes of the folar ſpots: the diffe-
rence is chiefly in fuperficial extent of length and breadth, their depth or
thickneſs is very fmall: fome have been fo large as, by computation, to co-
ver as much of the funs diſk as all Aſia and Africa, or even the ſurface of
the whole earth would do, if laid thereone: and fome have exceeded five
times the ſurface of our earthf. The diameter of a ſpot, when near the
middle of the difk, is meaſured by comparing the time it takes in paffing
over a croſs hair in a teleſcope with the time wherein the whole diſk of the
attenuta alla titubazion lunare.
a Iftoria e dimostrazioni di Galileo intorno alle macchie folari, in Roma 1613. b Letera di Galileo
c Aguilonius, in optica, Taquet, aftronom. Ricciolus, Almageſt.
Regnault, converfat. philofoph. d Opere di Galileo in Firenza. 1718. tom. 2. p. 224. e v. Hift.
f Smith's optics vol. II. p. 415.
d'Acad. 1719, 1720.
3 0 2
fun
472
BOOK 3.
ASTRONOMY
fun paſſes over the fame hair: it may alſo be meaſured by the micrometer: by
either of theſe methods, we find how many times the diameter of the ſpot is
contained in the diameter of the fun. Spots are fubject to increaſe or dimi-
nution, and feldom continue long of the fame magnitude.
1149 The folar fpots are of various fhapes: in moſt of them there is a
deep black nucleus furrounded by a duſky cloud, whereof the inner parts next
the black are a little brighter than the outskirts: they change their ſhapes,
fomething in the manner that our clouds do, though not often with fo fud-
den changes: thus, what is of a certain figure to day fhall, to morrow, or
perhaps in a few hours, be of a different one; what is now but one ſpot ſhall,
in a little time be found broken into two or three, and ſometimes two or three
fpots fhall coalefce and be united into one. The author of this work, many
years fince, while he was viewing the image of the fun caft through a tele-
ſcope upon white paper, faw one roundiſh ſpot, by eftimation, not much leſs
in diameter than our earth, break into two, which immediatly receded from
one another with a prodigious velocity: this is a thing which I have not
met with mentioned by any writer as obferved while it was actually
doing; though many inftances occur of its being taken notice of after it
has been done.
1150 The number of ſpots upon the fun is very uncertain: fometimes
there are a great many, fometimes very few, and fometimes none at all:
Scheiner obſerved from 1611 to 1629; and fays he never found the fun quite
clear of ſpots, except a few days in december 1624: at other times, he
frequently faw 20, 30, and in the year 1625 he was able to count above 50
ſpots upon the fun at a time. In an interval afterwards of 20 years, from
1650 to 1670, ſcarce any were to be ſeen: fince that time, fome years have
furniſhed a number of ſpots, and ſeveral years have been quite without:
but fince the beginning of the laſt century not a year hath paffed wherein
there have not been ſome ſeen; and at preſent ſays Caffini, in his Elements
d'Aftronomie printed 1740, they are fo frequent, that the fun is feldom with-
out ſpots, and often fhews a good number of them at a time. From what
has been faid it is manifeft that the folar ſpots obferve no regularity, in
their ſhape, magnitude, number, or in the time of their appearance, or
continuance.
1151 The ſpots of the fun are not permanent, but are diffipated or diffolv-
ed and diſappear: this is contrary to the doctrine of Ariſtotle and his follow-
ers, who held that the heavenly bodies are not fubject to generation or decay:
fome ſpots laſt many days, others are very ſhort lived: Hevelius obſerved
one that arofe and vaniſhed in 16 or 17 hours: no ſpot hath been known to
laft
CHAP. 9.
473
ASTRONOMY
laft longer than one that, in the year 1676, continued upon the fun above FIG.
70 days: thoſe ſpots that are formed gradually are gradually diffolved; thoſe
that ariſe fuddenly for the moſt part fuddenly vaniſh. When a ſpot difap-
pears, that part where it was fituated generally becomes brighter than the
reſt of the fun, and continues ſo ſeveral days: on the other hand, theſe bright
parts, which are called faculæ, fometimes turn to ſpots.
1152 The folar fpots appear to have a motion which carries them crofs
the diſk of the fun: every ſpot, if it continues long enough without being
from
diffolved, appears to enter the difk of the fun upon the eaft fide, to go
half its way;
thence with a velocity continually increafing, till it has gone half its
and then to move flower and flower, till it goes off at the weft fide of the
diſk: after which, it difappears for about the fame fpace of time, that it
fpent in croffing the difk, and then enters upon the eaſt fide again, nearly in
the fame place, and croffes it in the fame track, and with the fame unequal
motion as before. This apparent inequality in the motion of the ſpots is
purely optical, and is in fuch proportion as demonftrates them to be carried
round equably, in a circle the plane of which continued paffes through, or
near to the eye of a ſpectator upon the earth: ſee § 264, 266. In reality
then, the ſpots do not change their places upon the fun, but adhere to his
furface, or float in his atmoſphere, very near his body; for if there be 20
fpots or faculæ upon him at a time, they all keep in the fame fituation in
refpect of one another, and, fo long as they laft, are carried round together
in the fame manner: by the motion of the ſpots therefore we learn, what
otherwiſe we ſhould not have known, that the fun is a globe, and has a
rotation round his own axis.
1153 Befides the real changes in the ſhapes of the ſpots mentioned § 1149,
there is another change of them which is purely optical, and is owing to
their being feen upon a globe differently turned towards us: if we imagin
the globe of the fun to have a number of circles drawn upon its furface all
paffing through his poles and cutting his equator at equal diſtances, thefe
circles, which we may call meridians, if they were vifible, would appear to
us at unequal diſtances, as in fig. 92. Now fuppofe a ſpot were round, and 92
and fo large as to reach from one meridian to another, it would
appear round
only at g, when it was in the middle of that half of the globe which is to-
wards our earth, for then we view the full extent of it in length and breadth:
in every other place, it turns away from us, and appears narrower, though
of the fame length, the farther from the middle; and at its coming on at a
and going off at n it appears as fmall as a thread, the thin edge of it being
all that we then fee. This apparent change of the ſhape in the folar fpots
is
474
воок 3.
ASTRONOMY
FIG. is another proof that the fun is a globe, and that the ſpots adhere to the
furface of the fun fo as to be carried round thereon, or float in the funs at-
moſphere, very near his ſurface.
1154 The rotation of the fun being known, we may confider his axis,
and poles, and their fituation: as alfo his equator, or a circle imagined to
be drawn upon that luminous globe equally diſtant from his poles: we may
alſo imagin leffer circles drawn thereon parallel to his equator.
The rotation of the fun is according to the order of the figns: that is,
any point upon the furface of that vaft globe turns round fo as to look
fucceffively at aries, taurus, gemini, &c. which is alfo the way that all the
primary planets are carried round the fun, though each of them in a plane a
little different from all the reft; as was fhewn § 638: here alſo we are to
obſerve that, the plane of the funs equator continued does not coincide with
the heliocentric orbit of any of the planets, but cuts every one of them in
a ſmall angle: it is neareſt to coincidence with the orbit of venus.
1155 The fun being a globe at a great diſtance from us, we always fee near-
ly half of that globe at a time, § 241, but the viſible half is continually chang-
ing, by the rotation of the fun, and the revolution of the earth in her orbit.
To fpeak accurately, we do not fee quite half the funs globe at a time,
we want fo much of it as the apparent diameter of the fun amounts to,
which, at his mean diftance, is about 32 minutes; fo much is the diameter
of the invifible part of the fun greater than that of the viſible part: for this
reaſon, a ſpot may be about two hours longer inviſible than it is viſible.
v. Caffini, Mem. d'Acad. 1701.
1156 As the earth revolves round the fun the fame way with the funs
rotation, the periodical revolution of a ſpot ſeen from the earth is longer
93 than it would appear if it were viewed by an eye at reft: thus, fig. 93, let
ABCD be the orbit of the earth, abcd the equator of the fun, let a be a ſpot
feen in the middle of the diſk by a ſpectator upon the earth at A: the funs
rotation, carrying the ſpot round through bed according to the order of the
letters, will in about 25 days bring it again to a: but, during that interval,
the earth will be got to B, and the middle of the diſk will be then at b: fo
that about two days more muſt be fpent before a ſpectator upon the earth
at c will view the fpot in the middle of the then apparent diſk at c. This
is much the fame cafe as that of the fynodical month being longer than the
periodical, mentioned § 959.
1157 The time between the entrance of a ſpot upon the diſk and its exit.
therefrom gives us nearly half the apparent period of the funs rotation ;
this is uſually about thirteen days: a ſpot that, after croffing the difk and
diſap-
CHAP. 9.
475
ASTRONOMY
diſappearing, returns again gives the whole time, but not with preciſion; FIG.
becauſe the ſpot may perhaps not keep all the while exactly in the ſame
place, but may have fome floating motion of its own upon the furface
of the fun there are not many inftances of fuch returning fpots; Scheiner
has not above 3 or 4 among his multitude of obfervations. Dom. Caffini,
taking notice that ſeveral ſpots had often appeared in the fame parallel,
thought fome particular places of the fun might be more difpofed than
others to fupply the matter of thoſe ſpots; and, if ſo, that they would not
move far from the place of their origin, juſt as the ſmoke of mount Etna, if
it could be feen from the fun, would always appear to return to the fame
place upon the diſk of the earth, every 24 hours, very nearly; fometimes a
little fooner, fometimes a little later, according as the ſmoke was driven, by
an eaſt or weft wind, from the place of its eruption: in confequence of this
fuppofition, he compared ſeveral large intervals between the appearances of
ſpots carried in the fame parallel, which he judged to be returns of the fame
fpots, arifing out of the fame place on the furface of the fun; and found
that 27 days 22 hours and 20 ſeconds was a common meaſure of thoſe in-
tervals, very nearly: this therefore he thought to be the period moſt pro-
per to be taken for an apparent revolution of the folar ſpots, and confe-
quently for the rotation of the fun, as ſeen from the earth. Theſe obſer-
vations were made in may and april, nearly in the fame time of the
and therefore are not much affected by the inequality of the earths motion.
The fame period is confirmed by J. Caffini, Mem. d'Acad. 1702.
year,
The time of the apparent revolution of a ſpot being known, the true
time of its going round upon the fun is thus found: in fig. 93, the arc AC, 93
which in the month of may, the earth goes through in her orbit in 27 days 12
hours and 20 minutes, is 26 degrees and 22 minutes: the arc ac is equal
to AC, by § 31: the apparent revolution of a ſpot is the whole circle abcda
or 360° with the addition of the arc ac of 26° 22′: which makes 386° 22′:
ſay then, as 386° 22′ is to 27d 12h 20', fo is 360° to 25d 15h 16, the true
time of the rotation of the fun, as it would be feen from a fixt ſtar.
1158 The angle of interfection between the planes of the funs equator
and the ecliptic is but fmall; Scheiner fays he never found it more than 8°
nor leſs than 6º, he therefore ſettled it at 7°: Rofa Urfin. p. 556. J. Caffini
makes it 7° Smith's optics v. II. 411.
1
The plane of the funs equator continued cuts the ecliptic in two oppo-
fite points; the 8° of II and the 8° of : thefe points are called the nodes
of the fun, Two points in the ecliptic 90° from the nodes, namely, the 8°
of * and the 8° of my may be called the limits. When the earth is in either
of
476
BOOK 3
ASTRONOMY
FIG. of the funs nodes, the equator of the fun, if vifible, would appear as a
ftrait line, by § 258: and, by reaſon of the vaſt diſtance of the fun from us,
all his parallels would alſo appear ſtrait lines, § 254: in every other ſituation
of the earth, the funs equator and parallels, if vifible, would appear as ellip-
fes by § 257: and theſe ellipfes grow wider the farther the earth is from the
nodes; and are wideft, when the earth is in one of the limits.
1159 In the preſent age, on the 18th of may, the earth is in the 8° of ↑
one of the nodes of the fun; and, confequently, the funs equator and paral-
94 lels, if viſible, would appear as ftrait lines, fig. 94: from that time, the funs
equator and every parallel begin to appear as half of an ellipfis convex or
fwelling towards the fouth, and growing every day wider, to the 20th of
95 auguft, where it is at the wideft, as in fig. 95; the earth being then in the
8° of *, one of the limits: immediately after, the apparent curvature of the
funs equator and parallels continually decreafes, to the 19th of november,
when they again appear as ſtrait lines; the earth being in the other node,
96 the 8° of I, fig. 96: from that time, the equator of the fun and parallels be-
come elliptical, convex towards the north, their curvature continually increaſ
ing, to the 15th of february, when the earth is arrived at the other limit, in the
8° of ™, and their curvature is again at the greateſt, fig. 97: from thencefor-
ward, their curvature continually decreaſes, to the 18th of may, when the
equator of the fun and the parallels again become ftrait lines.
97
94
1160 Every ſpot is carried round the fun in his equator, or in a parallel :
therefore the apparent motion of the ſpots upon the fun is rectilinear, every
year, in may and november; at which times the funs equator and parallels,
if viſible, would appear as ftrait lines: at all other times of the year, the ap-
parent motion of the ſolar ſpots is elliptical.
Scholium. When it is faid the apparent motion of ſpots upon the diſk of
the fun is rectilinear, the meaning is that it is not fenfibly otherwiſe; for,
accurately ſpeaking, this is true only for a moment, when the earth is in
one of the funs nodes: as the planes of the funs equator and parallels inter-
fect the ecliptic, immediately after the earth is paffed from a node, our eye
begins to be elevated above the planes of the funs equator and parallels, and
the apparent paths of the ſpots become elliptic, nor do we ſee a ſpot move
in a true ellipfis, for any confiderable time; but, by the continual change
in the elevation of our eye, the apparent path of a ſpot, every fubfequent
moment, becomes a part of a different ellipfis.
1161 On the 18th of may, and the 19th of november, when the earth is
in one of the nodes of the fun, the north pole of the fun n and the ſouth
95 pole s are both in the circumference of the vifible diſk, fig. 94 & 955 then
every
CH A P. 9.
477
ASTRONOMY
";
97
every parallel is divided into two equal parts by the plane of the diſk, proxime. FIG.
v. § 1155. From may to november, the north pole of the fun n is upon the vi-
fible diſk, fig. 95: then the parallels are divided unequally, fo that, there is 95
more than half of every north parallel, leſs than half of every fouth parallel
upon the viſible diſk; and confequently, during that half year, every ſpot
in a north parallel is vifible more than half the period of the funs rotation
every ſpot in a ſouth parallel, is vifible leſs than half that period: on the
other hand, from november to may, the fouth pole of the fun s is
upon the
vifible diſk, fig. 97: and every ſpot in a fouth parallel is viſible more than
half the period of the funs rotation; every ſpot in a north parallel is viſible
leſs than half that period. The difference between the time of a ſpot being
vifible, and the time of its being hid behind the fun, arifing from the une-
qual divifion of the parallels by the plane of the diſk, is greater the nearer
the earth is to one of the limits: leffer the nearer the earth is to one of the nodes
of the fun. As the earth does not move uniformly in her orbit, but flower in
aphelion, quicker in perihelion, this will make a difference in the apparent
motion of the folar ſpots; the difference arifing from this caufe is not 4 hours
in an apparent revolution,
1162 The 92 figure being the orthographic projection of meridians drawn
at equal diſtances upon the viſible half of the funs globe, it may be thought
thoſe meridians would fhew the apparent diurnal motion of the ſpots; ſo that,
for example, a ſpot which to day at noon is in the meridian marked with a,
ſhould to morrow at noon be in the meridian marked with b, the next day
in that marked with c, &c. but Scheiner fays, that, caſting the ſuns picture
upon paper through the teleſcope, the diſtance between the place of a ſpot
at noon any given day, and the place of the fame at noon the day immedi-
ately preceding or the day immediately following will be greater, when the
fpot is near the circumference of the diſk, than, according to the orthogra-
phic projection, it ought to be: this deviation of ſpots, he thought owing to
the refraction of the glaffes in the teleſcope being greater near the circumfe-
rence than in the middle: he was confirmed in this opinion, by finding that,
if ſpots were obſerved by letting the fun fhine through a little hole without
a glaſs upon a white paper held at a good diſtance from the hole, in a dark
room, their places would then be every day according to the orthographic
projection: but this method of obferving the folar ſpots he found was attend-
ed with great difficulties. Rofa Urfina, 1.4. c. 19.
1163 Scheiner has another proof that the deviation of the folar ſpots from
the orthographic projection, is caused by the different refraction of the glaf-
ſes of the teleſcope, by the following experiment: he pierced with a needle
3 P
in
92
478
воок 3
ASTRONOMY
rays of
FIG. in a thin plate of brafs 12 fmall holes at equal distances, as in fig. 98, and,
98 placing the plate before the glaffes in a ſhort teleſcope, let the fun thine
through, receiving the 12 bright ſpots upon a paper held ſo as the
the fun might fall perpendicularly thereon: here alſo he found the diſtances
between the bright spots near the outfide were greater than between thoſe
in the middle; whereas when he received them upon paper without any
glaffes, the fituation of the bright ſpots exactly correſponded to that of the
ſmall holes in the plate.
1164 The face of the fun, when clear of ſpots, feen by the naked eye
through a ſmoaked or coloured glaſs, or through a thin cloud, or the vapours
near the horizon, appears all over equally luminous; but, when viewed
through the teleſcope, the glaffes being fmoaked or coloured, befides the dif-
ference between the facule and the other parts, the middle of the diſk ap-
pears brighter than the outſkirts a: the light is darted from the middle more
directly towards us than from the fides: any faculæ appear more diſtinctly
near the fides, as being upon a darker ground there, than on the middle b.
1165 The ſpots, generally ſpeaking, may be faid to adhere to the fun, or to
be fo near him as to be carried round upon him uniformly; nevertheleſs, fome-
times, though rarely, a ſpot has been ſeen to move with a velocity a little diffe-
rent from the reft: fpots that were in different parallels have appeared to be
carried along not keeping always at the fame diftance, but approaching
nearer to each other; and, when two ſpots moved in the fame parallel, the
hindmoſt has been obferved to overtake and paſs by the other. The revo-
lution of ſpots near the equator of the fun, is ſhorter than of thoſe that
are more diftant from itd.
1166 There are various opinions about the nature and formation of the
folar ſpots. Some have thought that the fun is an opake body, mountain-
ous and uneven as our earth is, covered all over with a fiery luminous
fluid; that this fluid is fubject to ebbing and flowing, after the manner of
our tides; ſo as ſometimes to leave uncovered the tops of rocks or hills,
which appear like black fpots: and that the nebulofities about them are
cauſed by a kind of froth.
Others have imagined, that the fluid which fends us fo much light and
heat contains a nucleus or folid globe, wherein, are ſeveral volcanoes, that,
like Ætna or Vefuvius, from time to time, caft forth quantities of bitumi-
nous matter up to the furface of the fun, and form thofe fpots which
are ſeen thereon: and that, as this matter is gradually changed and confumed
a Scheiner, Rofa Urfin. p. 622.
c ibid. p. 559. & paffim, v. in indice Rofa
e Caffini elements d'aftronomie. liv. 2. c. I.
b ibid. p. 508.
Urfin. curfus inequalis, d Caffini Mem. d'Acad. Mai. 1730.
by
CHAP. 9.
479
ASTRONOMY
by the luminous fluid, the fpots diſappear for a time; but are ſeen to riſe
again in the fame places, when thoſe vulcanoes caft up new matter.
A third opinion is that the fun confifts of a fiery luminous fluid, wherein
are immerſed ſeveral opake bodies of irregular ſhapes; and that theſe bodies,
by the rapid motion of the fun, are fometimes buoyed or raiſed up to the
furface, where they form the appearance of ſpots; which feem to change
their ſhapes, according as different fides of thoſe bodies prefent themſelves
to our view.
The laſt opinion I ſhall mention is, that the fun confifts of a fluid in con-
tinual agitation; that, by the rapid motion of this fluid, fome parts more
grofs than the reft are carried up to the ſurface of that luminary, in like
manner as fcum rifes on the top of melted metal, or any thing that is boil-
ing: that theſe ſcums, as they are differently agitated by the motion of the
fluid, form themſelves into thofe different ſhapes which we ſee in the folar
fpots; and, befides the optical change, mentioned § 1153, grow larger, are
diminiſhed in their apparent magnitude, recede a little from or aproach
nearer to one another, and are at laſt entirely diffipated by the continual ra-
pid motion of the fluid, or are confumed thereby, or abforbed therein.
1167 The funs atmoſphere has been mentioned, and a ſhort defcription
thereof given, in the first volume of this work, § 762; Sir Ifaac Newton,
in his optics, p. 318, has let us know what his fentiments were upon this
fubject, in the modeft way of a query, in the words following,
"Qu. Do not great bodies conferve their heat the longeft, their parts heat-
"ing one another, and may not a great denfe and fixed body, when heated
beyond a certain degree, emit light fo copiouſly, as by the emiffion and
"re-action of its light, and the reflections and refractions of its rays within
"its pores to grow ftill hotter, till it comes to a certain period of heat, fuch
"as is that of the fun? And are not the fun and fixed ftars great earths vehe-
<c
mently hot, whoſe heat is conſerved by the greatneſs of the bodies, and
"the mutual action and re-action between them, and the light which they
"emit, and whoſe parts are kept from fuming away, not only by their fix-
"ity, but alſo by the vaſt weight and denfity of the atmoſpheres incumbent
"upon them, and very ftrongly compreffing them, and condenfing the va-
"pours and exhalations which arife from them? For if water be made warm
"in any pellucid veffel emptied of air, that water in the vacuum will bubble
"and boil as vehemently as it would in the open air in a veffel fet upon the fire
"till it conceives a much greater heat. For the weight of the incumbent at-
mofphere keeps down the vapours, and hinders the water from boiling,
"until it grows much hotter than is requifite to make it boil in vacuo.
3 P 2
"Alfo
66
480
BOOK 3.
ASTRONOMY
"C
<<
"Alfo a mixture of tin and lead being put upon a red hot iron in vacuo emits
a fume and flame, but the fame mixture in the open air, by reaſon of the in-
"cumbent atmoſphere, does not fo much as emit any fume which can be per-
"ceived by fight. In like manner the great weight of the atmoſphere which
"lies upon the globe of the fun may hinder bodies there from rifing up and
going away from the fun in the form of vapours and fumes, unleſs by
"means of a far greater heat than that which, on the furface of our earth,
"would very eaſily turn them into vapours and fumes. And the fame great
weight may condenfe thofe vapours and exhalations as foon as they fhall
"at any time begin to afcend from the fun, and make them prefently fall
"back again into him, and by that action increaſe his heat much after the
"manner that in our earth the air increaſes the heat of a culinary fire. And
"the fame weight may hinder the globe of the fun from being diminiſhed,
"unleſs by the emiffion of light, and a very ſmall quantity of vapours
"and exhalations."
CC
1168 To the funs atmoſphere may be referred the femita luminofa, or the
luminous path, an appearance difcovered by Dom. Caffini, in the fpring of
the year 1683; whereof he gave a ſhort account in the journal des fcavans
of that year, and a more particular one, after ten years obfervation of it by
himſelf and Fatio, in a treatiſe printed in 1693a. This light which is fome-
thing like the milky way, or that of the faint twilight, or the tail of a
comet, thin enough to let ftars be feen through it, feems to furround the
fun in the form of a lens the plane whereof is nearly coincident with the plane
of the funs equator: it is feen ftretched along the zodiac, and accompanies
the fun in his apparent annual motion through the twelve figns: each end
terminates in an angle of about 21°: the extent of it in length from the fun
to either of the angular points varies from 50° to 100°: it reaches beyond
the orbit of venus, but not fo far as the orbit of the earth: the breadth of it
near the horizon is alſo variable, from 12° to almoſt 30°: near the fun, where
it may be reaſonably fuppofed to be broadeft, it cannot be feen; this light is
weaker in the morning when day is coming on, than at night when darkneſs
is increafing, and diſappears in full moon light, or in ftrong twilight, and
therefore is not at all vifible at midſummer, in places fo near either of the
poles as to have their twilight all night long; but may be ſeen in thoſe places,
both morning and evening, in the middle of winter; as it may all the year
round, in places near the equator: in north latitude, it is moſt confpicuous
after the evening twilight, about the latter end of february; and, before
the appearing of the morning twilight, at the beginning of october: for at
a Decouverte de la lumiere celefte dans le zodiac
thoſe
page 481.
99
100
Book III.
South
101
102
103
104
West
105
106
こ
​107
1
88
Oct.
14.
East
D D D D D D
North
1
AIND
Of
1
CHAP. 9.
481
ASTRONOMY
thoſe times it ftands moft erect above the horizon, and is therefore cleareſt
from the thick vapours and the twilight. Befides the difference of the real
extenfion of this light in length and breadth, at different times, it is di-
miniſhed by the nearness of any other light in the fky: not to mention
that the extent of it will be differently determined by different ſpectators,
according to the different goodneſs of their eyes.
Caffini, enquiring into the cauſe of this appearance, mentions first that it
might be owing to a great number of ſmall planets furrounding the fun,
within the orbit of venus; but foon rejects this for a more probable ſolution :
namely, that as, by the rotation of the fun, fome groſs ſubſtances are caft up
upon his furface, whereof ſpots and nebulofities are formed; fo the great
rapidity wherewith the equatoreal parts of that luminary are whirled round
may throw out to a confiderable diſtance a number of particles of a much
finer texture, of ſufficient denſity to reflect light: now, that this light is
cauſed by an emanation from the body of the fun fimilar to that of the ſpots,
he thought was made probable by the following obfervation, that after the
end of the year 1688, when this light began to grow weaker, no ſpots ap-
peared upon the fun; whereas, in the preceding years they were often feen
there: and that the great inequality in the intervals between the times of the
appearance of the folar fpots has fome analogy to the irregular returns of
weakneſs and ſtrength in this light, in like circumftances of the conſtitution
of the air, and of the darkneſs of the ſky.
1169 Caffini was of opinion that this light in the zodiac, as it is ſubject
to great increaſe, at one time, and great diminution at another, may ſome-
times become quite imperceptible: and thought this was the cafe in the years
1665, 1672, and 1681, when he ſaw nothing of it, though he then furvey-
ed with great attention thoſe parts of the heaven where, according to his
theory, it muſt have appeared, if it had then been as vifible as it was in
other years. He cites paffages out of ſeveral authors both ancient and modern,
that make it probable it had been ſeen in former and latter ages; but had
not been enough attended to, or the nature of it examined into; it haď
been taken for the tail of a comet, or part of the twilight, or for a meteor of
fhort continuance: and he was fully convinced of its having appeared for-
merly, by a paffage in an Engliſh book of Mr. Childrey's, printed in 1661
wherein this luminous appearance is deſcribed in the words following:
"There is ſomething more, that we would recommend to the obfervation
"of the mathematicians; namely, that in the month of february, and a lit-
"tle before and after it (as I have obſerved for ſeveral years) about fix a
"clock in the evening, when the twilight has entirely left the horizon, a
"path
482
BOOK 3.
ASTRONOMY
FIG. "path of light tending from the twilight towards the pleiades, and touching
"them as it were, preſented it ſelf very plainly to my fight. This path is
"to be feen whenever the weather is clear; but beft of all in a night when
"the moon does not ſhine." And a little after: "I am apt to believe that this
phænomenon has been formerly, and will hereafter appear always at that
"abovementioned time of the year. But the cauſe and nature of it, I cannot
"ſo much as gueſs at; and therefore leave it to the enquiry of pofterity."
cc
99
CHAP. IO. BELTS AND SPOTS UPON THE PRIMARY PLANETS: THEIR
ROTATION ROUND THEIR OWN AXES: THEIR SHAPES.
1170 Whether faturn has a rotation round his axis or not has not been
certainly diſcovered; fome of the ſpots and obfcurities feen upon him have
been mentioned before, § 1132 and 1145, and are fuppofed to be owing to
the dark edge of the ring, the ſhadow of the ring, or fhadow of clouds float-
ing in his atmoſphere. In 1683, Dom. Caffini and Fatio, faw a bright ſtreak
upon faturn, which was not permanent as the dark belts are, but was viſible
one day and the next difappeared, when another came into view near the
edge of his diſk: this induced Caffini to think he might have a rotation,
whereby different parts of his body were expoſed to our view: if there be no
rotation, this piece of a bright belt muſt be ſubject to change: that the re-
volution of his ring round his body is probable, has been already obferved,
§ 1133: the diſtance of this planet from our earth is fo great, that we can
hardly hope to know much more of it than we do.
1171 The belts of jupiter are dark broad ftreaks that appear cross his diſk,
100 fig. 99, 100, 101, 102: fo called becauſe they girt the body of that planet quite
IOI round: they are not to be ſeen but by an excellent teleſcope: Ricciolus men-
102 tions Fontana and two other Neopolitans as the firft that diſcovered thema;
but Dom. Caffini was the firſt that gave a good account of themb: the number
of them is variable, fometimes eight have been ſeen at a time; at other times
not above oned: they are generally parallel to one another, though not al-
ways fo; for, a piece of a belt has been ſeen in an oblique pofition to the reſt,
101 as in fig. 101: they vary in their breadth; for, one belt has been obſerved
to be grown a good deal narrower than it was, when a neighbouring belt has
been increaſed in breadth, as if, being a fluid, one had flowed into the other*:
in favour of this opinion, a part of an oblique belt was obſerved to lie fo as
102 to form a communication between them, fig. 102. At one time, the belts
a Almageſt. 1. 7. c, 2. b Hift. d'Acad: R tom, 2. c u. fig. 100,
& Mem. d'Acad. 1714. e ibid.
have
CHAP. 10.
483
ASTRONOMY
have continued without fenfible variation for near three months; at another FIG.
time, a new belt has been formed in an hour or two.
1172 On the 9th of may 1664, Dr. Hook, with a good 12 foot teleſcope, ob-
ferved a ſmall ſpot in the biggeſt of the three obſcure belts of jupiter, and
obſerving it from time to time, he found that within two hours the ſaid ſpot
had removed from eaſt to weſt, about half the length of the diameter of ju-
pitera. Near one of the belts, the largeſt and that ſeen moft frequently,
Caffini, in the year 1665, faw a spot that appeared round, and moved with
the greateſt velocity when in the middle, but was narrower and moved
flower the nearer to the circumference of the difk: theſe circumftances
ſhewed that the ſpot adhered to the body of jupiter and was carried round
upon it; it continued thereon till the year following, long enough to deter-
min the periodical time of jupiters rotation round his own axis to be nine hours
fifty fix minutes: this principal, or ancient ſpot as it is called, is the largeſt
and of the longeſt continuance of any hitherto known, has appeared and
vaniſhed no fewer than eight times, between the years 1665 and 1708:
from the year laſt mentioned, it was invifible till 1713: the longeſt time
of its continuing to be vifible was three years, and the longeſt period of
its diſappearing was from 1708 to 1713: it ſeems to have fome connection
with the principal fouthern belt; for the fpot has never been ſeen when that
diſappeared, though that belt has often been vifible without the ſpot. Befides
this ancient fpot, Caffini, in the year 1699, ſaw one of lefs ftability, that
did not continue of the fame fhape or dimenfions, but broke into ſeveral
fmall ones, whereof the revolution was but 9h 51: and two other ſpots
that revolved in 9h 52. To compare thefe changes in the belts and fpots,
with what would appear upon the diſk of our earth viewed at ſuch a dif-
tance as brought it to the fize of jupiter, it has been ſaid, the great ocean that
environs our earth would reſemble the principal belt of jupiter; the medi-
teranean one of his broken belts; the cafpian fea a large fpot: fome of our
largeſt iſlands the bright spots feen in the belts of jupiter, fig, 100: the 100
clouds ſtretched round the equator of the earth his changeable belts b.
1173 The rotation of jupiter, like that of the fun, is according to the
order of the figns: the belts of jupiter are parallel to his equator: the plane
of his equator is coincident with the plane of his orbit, or very nearly fo:
there is therefore hardly any difference of feafons, but rather a perpetual
equinox in that planet.
Some aftronomers have thought the revolution of the planets round their
axes, were accelerated as they drew near the fun; contrary to this opinion,
a Philofoph. tranfact. n. 1.
b Mem. d'Acad. 1692.
the
484
ASTRONOMY
BOOK 3
the rotation of jupiter has been found a little quicker near his aphelion than
near his perihelion ª.
The figure of jupiter is not exactly globular, but an oblate fpheroid; his
equatoreal diameter being longer than that between his poles: the difference
between them is great enough to be perceived by the teleſcope, through which
his diſk appears an oval; and, meaſured by the micrometer, the longeſt di-
ameter is found to be to the ſhorteſt nearly as 13 to 12 b.
1174 In the beginning of february 1666, Dom. Caſſini, at Bologna, with
a teleſcope of Campani of 16 feet and, faw spots in mars; and, continu-
ing to obferve them for about a month, found they came every day into the
fame fituation, in the fame hour as on the day immediately preceding, but,
later by 40 minutes: fome aftronomers at Rome, with longer teleſcopes
made by Eustachio Divini, obferved mars about the fame time, and gave
out that he made his revolution in 13 hours: Caffini thought they were too
hafty in pretending to fettle the period of his rotation from five or fix obſer-
vations only, whereas, he could not from a much larger number made by
himſelf, determin certainly whether 24 hours and 40 minutes were the mea-
ſure of one rotation only, or of two: all that he could be poſitive in was,
that the ſpots returned to the fame fituation in 24h 40. After more obſer-
vations, he publiſhed a ſecond piece, wherein he brought ſeveral proofs to
ſhew that mars turns round his axis only once in 24h 40; and that they who
had afferted his turning round in 13 hours, had fallen into that miſtake for
want of diſtinguiſhing the oppofite fides of that planet from one another;
for, the oppoſite ſpots ſeem to have been pretty much alike: this, probably,
was the reafon of Caffini's doubt at first, and that, Dr. Hook, who obferved
thoſe ſpots in London the fame year in march, had the fame doubt whether
they went twice round in 24 hours, or only once. Caffini, on this occafi-
on, printed a ſmall treatiſe upon the ſubject with figures, whereof an ab-
ſtract may be feen in the journal des fcavans for the month of
may 1666.
1175 In 1670 Caffini obferved the fame ſpots at Paris, and found their
periodical revolutions the fame as he had fettled them four years before at
Bolognad. The ſpots of mars were again obſerved in fubfequent oppofitions,
and, in particular, feveral days in 1704, by Maraldie, who took notice that
the ſpots were not always well defined, and that they often changed their
form, not only in the ſpace of time between one oppofition and another, but
even within a month: that, however, fome of them continued of the fame
a Maraldi Mem. d'Acad. 1714.
c Lowthorp, Phil. tranf. abr, vol. 1. p. 423.
e Mem. d'Acad. 1706.
b Newton. princip. 1. 3. prop. 19.
d Du Hamel, reg. fcient. Acad. hift. ad ann. 1670.
·
form
CHAP. IO.
485
ASTRONOMY
form long enough to aſcertain their periods: among thefe, in the year 1704 FIG.
there was an oblong ſpot not unlike one of the broken belts of jupiter, that
did not reach quite round the body of mars, but had, not far from the mid-
dle of it, a ſmall protuberance towards the north, fo well defined as to
enable him to ſettle the period of its revolution at 24h 39; only one mi-
nute leſs than Caffini had determined itª, fee fig. 103.
103
1176 On the 27th of auguft 1719, mars in oppofition was within 2° of his
perihelion, nearer to the earth than he had been in the former obfervations;
whereby his magnitude and brightneſs were fo much increaſed, that, by
common ſpectators, he was taken for a new ſtar: among other ſpots then
feen upon mars through a teleſcope of 34 feet, by Maraldi, there was a
long belt that reached about half way round him, that was not parallel to his
equator, as the belts of jupiter generally are, but very much inclined to it,
fig. 104: to one end of it another ſhort belt was joyned, ſo as to form be- 104
tween them an angle a little obtuſe, fig. 105: this angular point was obferv- 105
ed a little eaſt of the middle of the diſk, auguſt 19 and 20 at 11h 15; and 37
days after on ſeptember 25 and 26, returned to the fame fituation: this in-
terval, divided by 36 the number of revolutions contained therein, brings out
the period of one revolution 24h 40': this period was verifyed by another
ſpot upon mars of a triangular ſhape, one angle whereof was towards the
north pole, and the baſe towards the ſouth: this ſpot on the 5th and 6th of
auguft, appeared as in fig. 106; and after 72 revolutions returned to the
fame fituation, on the 16th and 17th of octoberb.
1177 Befides the dark ſpots, there is a fegment of the globe of mars round
his fouth pole, of a brightneſs ſo much fuperior to that of the other parts, as
to make it appear beyond them, as if it were a portion of a larger globe:
this is from the fame caufe as makes the bright part of the moon near con-
junction, ſeem to be a fegment of a globe of a larger diameter than the ob-
fcure part; namely, becauſe a luminous object makes a ftronger impreffion
upon the retina than an opake one, fee § 585. The bright ſpot now men-
tioned Maraldi fays had been taken notice of for 60 years, and is more per-
manent than any of the other ſpots of mars; this ſegment or zone is not all
of equal brightneſs, for more than one half of it is brighter than the reſt;
and that part which is leaft bright, is fubject to great changes, and has
fometimes diſappeared. There has alſo been fometimes a like luminous
has been
zone feen round the north pole of mars, which in different
of different brightneſs c.
years
106
a Mem. d'Acad. R. 1706,
b Mem. d'Acad. 1720.
3 Q
c ibid.
1178
486
BOOK 3
ASTRONOMY
FIG.
·107
1178 The earliest mention I have met with of ſpots in venus is in a col-
lection of letters printed at Paris, in 1665a; in one of which Mr. Auzout,
relates his having received advice from Poland that Mr. Burattini had, by
means of large teleſcopes, feen upon the planet venus fpots fimilar to thoſe
upon the moon.
1179 In 1667 Dom. Caffini in a letter to Mr. Petit, gives an account of his
having for a long time through an excellent teleſcope of Campani, carefully
obſerved venus, in order to find whether that planet did not turn round up-
on her axis with ſuch a motion as he had before diſcovered in jupiter and
mars. He fays that, even when the air is quiet and clear, the fpots upon
venus appeared faint, irregular, and not well defined; fo that it is difficult
to have ſo diſtinct a view of any of them as to be certain one fees the fame
again in a fubfequent obfervation; whereby a judgement might be formed
whether ſhe has a rotation or not: that this difficulty is increaſed, becauſe,
1, when venus is in her inferior femicircle, the propereft time on account
of her being then neareſt to us, fhe muſt be viewed through the thick va-
pours near the horizon:
2, if we would obferve her at fome height
above thoſe vapours, it can be only for a fhort time: 3, when ſhe is very
low in her inferior circle, and neareſt to the earth, the enlightened part of
her, the only part viſible, is too ſmall to diſcover any motion thereon. He
therefore thought he ſhould fucceed better in his obſervations, when venus
was near her mean diſtance, and ſhewed about half of her enlightened he-
miſphere, and when he could have a longer view of her at fome height above
the grofs vapours.
1180 The first time he perceived any thing whereby he could hope to find
out her motion, was the 14th of oct. 1666, at 5h 45 in the evening, when he
faw a bright ſpot near the fection b, at a good diſtance from the center of
the planet, towards the north: at the fame time, he took notice of two
dark oblong ſpots near the weft fide of the diſk, all as reprefented in fig. 107.
He could not then view that bright ſpot long enough to conclude any thing
about the planets motion; and, all the remaining part of the year, had not
one evening clear enough for his purpoſe: and, though in the following year
1667, from feb. 24, he took all the opportunities of clear air that he could
have, he faw only fome obſcure ſpots not well defined, till the 20th of april
in the morning; and then, a quarter of an hour before funrife, he began to
fee again upon the diſk of venus, now about half enlightened, a bright part,
a Journal des fcavans, vol. 1. p. 216. In the fame volume of the journal des ſcavans p. 287 it is faid
Burattini diſcovered inequalities in venus, like thoſe in the moon. See alſo Phil. tranf. n. 10.
b So he calls the limit between the light and dark.
near
CHAP. IO.
487
ASTRONOMY
109
near the ſection, diſtant from the ſouthern horna a little above a fourth part FIG.
of the diameter of the diſk, and near the eaſtern edge; he took notice alſo
of a darkiſh oblong ſpot, nearer to the northern than to the ſouthern horn,
as in fig. 108: at funrife, he perceived the bright part was advanced farther 108
from the ſouthern horn than when he firſt obſerved it, being now got about
a third of the diameter diftant therefrom, as in fig. 109: he fays he
part
had then a good deal of fatisfaction at finding an evident proof of the pla-
nets motion; but was furpriſed to find this motion to be from fouth to
north, in the lower part of the difk; and from north to fouth, in the upper
part; from whence we make the beſt judgement which way any rotation is
determined, becauſe we have no example of any ſuch motion, except in the
librations of the moon b. On the next day, the 21ft of april at ſunriſe, the
bright part was a good way off the ſection, and was diſtant from the ſouth-
ern horn a fourth part of the diameter of the diſk, fig. 110: when the 110
fun was 8° 6′ high, it ſeemed to be got beyond the center, and was cut
through by the ſection: and when the height of the fun was 7 degrees, the
fection cut it in halves, as fig. 111, which fhewed its motion to have fome 111
inclination towards the center.
1181 On the 9th of may, a little before ſunriſe, he again faw the bright
fpot near the center, a little to the northward, with two obfcure ſpots fi-
tuated between the fection and the circumference, at a diſtance from one
another equal to that each of them was at from the neareſt horn: the wea-
ther being clear, he obſerved, for an hour and half a quarter, the motion of
the bright spot, which feemed to be exactly from fouth to north, without
any ſenſible declination, to eaſt or weft. At the fame time, he perceived
a variation in the darkiſh ſpot, too great to be accounted for by any opti-
cal cauſe, as may be feen in fig. 112, 113.
On the 10th and 13th of may, before ſunriſe, he ſaw the bright ſpot be-
tween the northern horn and the center, and took notice of the fame irre-
gular change of the darkiſh ſpots: but when venus began to be a little far-
ther from the earth, it became very difficult to obſerve theſe appearances.
Caffini was very careful not to ſpeak his opinion of theſe phænomena
ſo affuredly as he had done about the ſpots of jupiter and mars; for theſe,
a He calls the angular points that terminate the fection horns, though venus was not then horned.
b Caffini expected to find the rotation of venus like that of jupiter and mars, which planets have their
axes nearly perpendicular to their reſpective orbits, and turn round according to the order of the figns, fo
that in each of them the motion of the inferior half of their reſpective globe, or that part next the fun is
from east to west; in the fuperior half from weſt to eaft; whereas in venus, the axis of rotation is ſo near
coincidence with the orbit, that in one half of her globe the motion appears from fouth to north; in the
other half from north to ſouth.
112
113
3 Q2
fays
488
BOOK 3.
ASTRONOMY
fays he, I could attentively obferve for a whole night, when thofe planets
were in oppofition to the fun : I could ſee them return to the fame fituation,
and confider their motion during fome hours, and judge whether they were
the ſame ſpots or not, and what time they took in turning round: but it
was not the fame cafe with regard to the fpots of venus: for they can be
obferved for fo ſhort a time only, that it is much more difficult to know with
certainty when they return into the ſame fituation: I can however, ſays he,
(fuppofing that the bright ſpot which I obferved on venus, and particularly
this year, was the fame) fay that the finiſhes her motion, whether of ro-
tation or libration, in leſs than a day; ſo that in 23 days nearly, the ſpot
comes into the fame fituation on the fame hour of the day, though not with-
out fome irregularity. Now (fuppofing the bright ſpot obferved to be always
the fame) whether this motion is an entire turning round or only a libration
is what I dare not poſitively affirm. Thus far Dom. Caffini, in the journal
des fcavans for the year 1667, as corrected by his fon from fome manu-
fcripts of his father, in the memoires of the R. Acad. for the year 1732.
1182 From this time for near fixty years, we meet with no account of
ſpots in venus: in 1669, Caffini upon the invitation of the French King went
into France, and was made a member of the R. Academy: not long after,
mars and venus being in perigee, he obferved both thoſe planets at Paris,
faw the ſame ſpots on mars that he had ſome years before feen at Bologna,
and verified the period of his rotation the fame as he had formerly fettled it;
but could not perceive any ſpots upon venus: perhaps, fays Du Hamela, the
fluctuation of vapours near the horizon hindred his feeing them.
1183 On the 9th of february 1726 Bianchini, with teleſcopes of Campani
of 90 and 100 Roman palms, began to obſerve venus at the altitude of 40°
above the horizon, and continued his obſervations till, by the motion of ſe-
veral ſpots thereon, he determined the axis of her rotation to be fo fituated that
the north pole pointed at a circle of latitude drawn through the 20° of, ele-
vated 15° or 20° above the orbit of venus or the ecliptic. This is very diffe-
rent from jupiter and mars, which have their axes nearly perpendicular to
their orbits, and by their rotations are fo carried round, that the lower half,
or that towards the fun, of each of them appears to go from eaft to weft; the
upper half, or that averſe from the fun, goes from west to eaſt: whereas in ve-
nus the motion of the ſpots in the lower half is from north to fouth. All this is
ſet forth at large in his book intituled Hefperi et Phoſphori nova phænomena,
wherein he gives alfo a curious view of a remarkable ſpot on the moon:
deſcribes his method of obſerving the parallax of venus; and exhibits vari-
a Reg. fcient. Acad. hifter, ad ann. 1670,.1671.
ous
Page 489.
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CHAP. 10.
489
ASTRONOMY
ous figures of the ſpots on that planet; whereof, ſeven of the largeſt he look- FIG.
ed upon to be feas,. and complimented the King of Portugal and other great
perfonages by calling thoſe fuppofed feas by their names.
11.84 In Bianchini's obfervations, we do not find any one of them continued
long enough to diſcover any ſpot to have been, at the end thereof, in a diffe-
rent fituation from what it was in at the beginning; but, at the diſtance of
two days, and of four days, he found the ſame ſpot advanced ſo far that he
concluded it muſt have gone round at the rate of about 15° in a day: this
advance would fhew that venus turned round either once in about
24 days,
or in about 23 hours, but would not afcertain which of thoſe two was the
period: for, if an obſerver ſhould at a given hour, ſuppoſe at 7 in the
evening, mark exactly the place of a ſpot, and at 7 in the evening of the
day immediately fubfequent, find the ſpot advanced 15°, he would not,
from thoſe obſervations, be able to determin whether the ſpot during that
interval of 24 hours had advanced forward only 15°, or had gone once quite
round with an addition of 15° more, in part of another rotation.
1185 of theſe two periods Bianchini afferts the rotation of venus to be in
24 days 8 hours. The chief proof that he brings of this is an obſervation he
made of three ſpots A B C being in the fituation as repreſented in fig. 114, 114.
when he and ſeveral perfons of diftinction viewed them for about an hour,
during which they could not perceive any change of place in them: venus
then being hid behind the Barbarine palace, their view of her was interrupted
for almoſt three hours; at the end whereof they could again place the tele-
ſcope fo as to have a fight of her fpots, which they found had not-fenfibly
changed their fituation: now (fays he) if her rotation were ſo ſwift as to go
round in 23 hours, in this fecond view three hours after the firſt, the ſpots
muſt have been advanced near 50 degrees; fo that the ſpot c would have
been gone off at R, the ſpot B would have fucceeded into the place of c, the
fpot. A into the place of B, and there would have been no more than two
ſpots to be ſeen, A and B.
1186 Caffini the ſon, in a memoire of the year 1732, allows the obſervations -
of Bianchini to be good, but not conclufive for the period of 24 days 8 hours,
againſt the period of 23 hours, which had been conjectured rather than afferted
by his father, and was generally received by aſtronomers: he fhews that du-
ring the three hours interruption, the ſpot c might be gone off the diſk, and
the ſpot в got into the place thereof, where, being near the edge, it would:
appear leſs than when in the middle: that A fucceeding into the place of B
would appear larger than it had done near the edge, and that another ſpot
might come into the place. of A.; for that there were other ſpots on the globe
1
of
490
ASTRONOMY
BOOK 3.
of venus, befides the three marked in the figure with A, B, C, and particularly
one which by the rotation of the planet, would be brought into the place
of A, appears by the figures given by Bianchini: that if the rotation of venus
be ſuppoſed to be in 23 hours, it will agree with the obſervations of Bianchini,
as well as thoſe of his father; whereas, if it be in 24 days 8 hours, we muſt
abfolutely reject the obfervations of his father as erroneous; and concludes.
with telling us that venus had frequently been obſerved in the moſt favour-
able times for that purpoſe, by the late Maraldi and himſelf, with excellent
teleſcopes, one of 80 and another of 100 feet focus, but they had not been
able to fee any diftinct ſpot upon her: perhaps thoſe ſeen by Bianchini had
diſappeared, or the air in France was not clear enough; which laſt might
be the reafon that his Father never could in France, even with the longeſt
teleſcopes, ſee thoſe ſpots in venus which he had ſeen in Italy. Fontinelle's
remarks upon this occafion are very juft, that we can hardly think fo able
an obferver as Dom. Caffini could be guilty of fo grofs a miſtake, as to ima-
gin he faw the ſpot on venus move fafter upon her diſk than it was poffible
it fhould do: and that an hypothefis in aftronomy which accounts for the
obfervations of two good obfervers is certainly preferable to fuch an one as is
confiftent with the obfervations of only one of thema.
Before I leave this fubject, I muſt remark that neither Caffini nor Bian-
chini take notice in their writing s of any indentings in the curve which di-
vides the illuminated part of the diſk of venus from the dark, nor do they
expreſs any ſuch thing in their figures; whereas, in fome views of venus in
Fontana and Ricciolusb, this curve is indented; and it has from thence been
concluded that venus was mountainous, as the moon was fhewn to be § 996.
1187 The rotation of the earth round her own axis has been mentioned
already, § 296, and will be thought fufficiently proved, if we confider how
utterly improbable it is that the heavenly bodies ſhould be whirled round
us with ſuch inconceiveable rapidity as they muſt be, if the earth has no
rotation.
1188 A great circle upon the earth has been fhewn to meaſure near 25
thouſand miles, § 457: by the earths rotation, every place upon the ſurface
of the earth under the equator goes this round in 24 hours, and confequent-
ly moves above a thouſand miles in an hour: the diſtance of the earth from
the fun, is computed at 82 millions of miles, § 917; the circle then where-
in the fun muſt go round us every 24 hours, if the earth has no rotation, is
above 492 millions of miles; fo that, if the fun goes round us every 24 hours
a v. Hiftor. et mem. de l'Acad. ann. 1732. See alfo Smith's optics, book 4. chap. 2.
↳ Almageft. 1. 7. c. 2. Lowthorp's Phil. tranfa&t. abr. vol. I. p. 425.
as
CHAP. IO.
491
ASTRONOMY
as he appears to do, he must go at the rate of above 20 millions of miles in
an hour. The diſtance of the ſtars from our earth, is computed to be four
hundred thousand times greater than the diſtance of the fun, § 837: if then,
the ſtars go round us every 24 hours, as they appear to do, they muſt,
in that ſpace of time, go round in a circle four hundred thouſand times
as great as the circle of the fun; that is, they must go at the rate of above
8 millions of millions of miles in an hour. This computation fhews how
much greater the probability is that the earth turns round her axis, than that
the heavens revolve round the earth.
1189 The rotations diſcovered in jupiter mars and venus, are ſo many ar-
guments from analogy that the earth has the like, as alſo that mercury turns
round his axis, though this planet is always ſo near the fun and furrounded
with ſo ſtrong a twilight, that if he has any ſpots they cannot be obſerved.
Let us now confider what effect rotation would have upon the shapes of the
planets, fuppofing they were ever in a fluid ftate, or contained a fluid en-
clofed in a cruft; after premifing the following lemmas.
1190 Lemma 1. Every body that is whirled round a center, has a centri-
fugal force, that is, a tendency to fly off farther from the center in a tangent
to the circle of its motion: this is evident from the motion of a ſtone
thrown out of a fling.
Lemma 2. The greater the velocity is wherewith any body is whirled
round, the ſtronger is the centrifugal force thereof: this is evident by the
fame experiment of a fling.
1191 The French aſtronomers, upon meaſuring the earth in the manner
mentioned § 470, found the degrees on the meridian to be lefs on the north fide
of Paris than on the fouth; and from thence concluded, rightly, if the
pre-
miſes had been true, that the ſhape of the earth was oblong, fomewhat like
an egg, having its diameter longer at the poles than at the equatorª: but this
opinion was not univerfally received by the members of the R. Academy:.
it was confidered that, 1, if the earth were formed into a globe by the mutu-
al attraction of all its parts, upon its having a rotation, the centrifugal force
would cauſe the equatoreal parts to riſe higher than the reſt, and give it the
fhape of an oblate spheroid, a little flatted at the poles like a turnep: 2, that
this ſhape is manifeftly feen in jupiter, § 1173, the rotation whereof is
much ſwifter than that of our earth: 3, that a clock which keeps true time
in France goes too flow when carried near the equator; and muſt, in order:
to rectify it have the pendulum fhortened, to compenfate the diminution of
its gravity: 4, that from theſe arguments Hugens had concluded the earth to
a Suitte des mem. ann. 1718. See § 471.
be
492
BOOK 3
ASTRONOMY
be flatted as above mentioned, and Sir Ifaac Newton had demonftrated it to
be ſtill flatter than Hugens made it ª.
1192 To decide this controverſy about an affair not purely fpeculative
but of fome importance in aſtronomy and navigation. ſeveral of the mem-
'bers of the R. Academy were by order of the French King fent, one part
of them into Peru, to meaſure the length of a degree under the line; the
other part into Lapland, to meaſure a degree as near the pole as they could
conveniently go. They who went northwards, though they fet out later
than thoſe upon the fouthern expedition, returned before them, having a
ſhorter voyage to perform: a detail of their obſervations may be ſeen in a
treatife publiſhed by Maupertuis, which he read to the Academy in 1739,
and is printed in the memoires of that year b. He therein fhews that a degree
meaſured under the polar circle is about 400 toiſes longer than a mean degree
in France, and confequently that the earth is an oblate ſpheroid. Upon the
return of thoſe gentlemen to Paris, the ſhape of the earth coming out fo dif-
ferent from what had been determined by former obfervations, it appeared
neceſſary to review the meridian of the Royal obfervatory; accordingly, the
Count de Maurepas, a great encourager of the ſciences, procured an order
of the King for that purpoſe: how they proceeded in this operation Maupertuis,
who was one of the perfons employed, gave an account in a treatiſe cited
in the margin c.
1193 Picard, was believed to have meaſured his fundamental baſe with
fuch accuracy that it was taken for granted they might depend upon its cor-
rectneſs, as Caffini had done, in his meaſure of the earth mentioned § 471,
but it was thought neceffary to meaſure again an arc in the heaven, though
- meaſured before by very able obſervers; becauſe the aberration of the ſtars,
a new element lately diſcovered by Dr. Bradley, was now to be taken into
the account, and they had got an inftrument fuperior to any before made
uſe of; it was a ſector divided by Mr. Graham, the correctneſs of which they
had fufficiently experienced, in their northern expedition.
1194 The church of Notre Dame in Paris and that of N. D. in Amiens
lie fo nearly under the fame meridian that they differ only three minutes of
a degree in longitude, the arc between the zeniths of theſe two churches
was, by a great number of obfervations of the ſtar á in Perfeus and the ſtar
Y
a Hugens made the length of the axis of the earth to be to the equatoreal diameter as 577 to 588.
Hift. d'Acad. ann. 1742: Sir Isaac Newton, as 178 to 179, princip. math. prop. 18. b Figure de la
terre determine par obfervations au circle polaire &c. par Maupertuis. This is tranflated into engliſh.
c Degre du meridien entre Paris et Amiens determine par la meaſure de Picard et obſervations de
Maupertuis, Clairaut, Camus, le Monnier, &c. a Paris 1740.
of
CHA P. IO.
493
ASTRONOMY
of Draco, found to be 1° 2′ 28″: the diſtance between thoſe two places upon
the earth, according to their meaſure, is 59530 toiſes; this meaſure brings
out the length of the first degree north of the obfervatory of Paris 57183
toiſes, which is 123 toiſes more than Picard made it, and exceeds by a ſtill
greater number of toifes what Caffini determined in his book of the mag-
nitude and figure of the earth, quoted § 471: comparing this degree in
France with the degree meaſured under the polar circle, found by them of
57437,9 toifes, they concluded the earth to be flatted at the poles, and that
the axis is to the diameter at the equator as 177 to 178.
1195 In 1739 M. Caffini de Thury grandfon to Dom. Caffini affifted by
M. De la Caille, undertook a review of the meridian of France: an account
of their procedure therein may be ſeen in the hiſtory and memoires of the R.
Academy of 1740, and more at large in his book printed in 4to at Paris
în 17442:
they divided the whole length of the meridian from Perpig-
nan to Dunkirk into four parts, not equal, but fo as was moſt convenient
for their obfervations; they meafured in each part, with great accuracy, a
fundamental baſe of a confiderable length, from which they conſtructed a
fufficient number of triangles; in theſe they did not admit any very acute
angle, nor did they conclude the quantity of any one angle from the mea-
fures of the other two, but actually meaſured every angle with a good in-
ftrument: by comparing their own meaſures with thoſe of Picard, they
found he had certainly made ufe of too fhort a toife, though he fays in his
book he took it from the ftandard in the chastelet: they found that the pro-
per correction would be to take from his numbers at the rate of one toife in
1000. In examining the meridian they found only 6" difference, this is as
near preciſion as can be expected; fince an error of one fecond in time will
produce one of 11" or 12" in the pofition of a meridian: this by the
fhews the meridian was not fenfibly changed fince Picard's time.
way
1196 The meridian of France is extended between 42 and 51 degrees of lati-
tude; by meaſuring this diſtance and the correſponding arc in the heaven by
piecemeal, they brought out the number of toiles contained in a degree of
the meridian cut through in the middle by the parallel of 45°, to be 57045:
this is the mean degree, for 360 fuch are contained in the whole circumfe-
rence of a meridian, whether the earth be perfectly ſpherical, or an oblong,
or oblate ſpheroid: in all theſe three cafes, the degree under the parallel of
45° latitude would be the mean, being in the middle between the equator
and the pole. They found the degrees on the meridian confifted of a greater
number of toiſes as they went nearer to the pole, in all their obſervations
a La meridienne de l'obfervatoire Royal de Paris verifiee &c. par M. Caffini de Thury, a Paris 1744.
except
3 R
}
1
494
BOOK 3
ASTRONOMY
except one, wherein they imagined fome miftake might have been made.
1197 The difference between degrees immediately fubfequent on the me-
ridian was found ſo ſmall, that they reſolved to inveſtigate the length of a de-
gree in a parallel: for, fuppofing the fhape of the earth to be regular, eve-
ry parallel would be larger, contain a greater number of toifes, if it were an
oblate ſpheroid; lefs, if it were an oblong one, than if it were a perfect globe:
they therefore meaſured a longer fundamental bafe than any before made
uſe of in France, and conſtructing four triangles thereon, they took the diſ-
tance between two mountains, Sette in Languedoc and Saint Victoire in Pro-
vence, both very nearly fituated in the parallel of 43° 32'; and found the
difference of their longitudes by the following method: Cafini at Sette and
de la Caille at Saint Victoire, having each of them a clock well regulated
to the meridian of his ſtation, a quantity of gunpowder was fired at a third
place within view of both obfervers, and the time of the flaſh noted by
the clocks; this gave the difference in longitude of the two ſtations in mi-
nutes and ſeconds of an hour, which was eaſily turned into degrees minutes
and ſeconds by § 316. By this obſervation it appeared that a degree in the
parallel of 43° 32′ conſiſts of 260 toifes more than it would do if the earth
were perfectly ſpherical, of fuch dimenfion as. anfwers to the number of
toiſes that had been found by them in a degree of the meridian in the lati-
tude of 43° 32'. From all their obfervations theſe gentlemen concluded the
earth to be flatted at the poles, and the length of the diameter at the poles
to be to the diameter at the equator as 168 to 169.
1198 The academicians fent to Peru were M. M. Godin, De la Condamine,
and Bouguer, they were accompanied by a phyſician who was to be employ
ed in ſtudying the natural hiſtory of the country, a furgeon, an engineer, and
feveral perfons who were to affift in defigning, calculating, reconnoitering the
country, and taking care of their inftruments: as they were to go into places.
under the dominion of the King of Spain, where ftrangers are not eafily
permitted to come, it was neceffary for them to have paffports, which, at
the request of the French King, his Catholic Majefty not only readily grant-
ed, but gave directions alſo to his Viceroys and other officers to favour them:
on all occafions, and accommodate them with what they ſhould ſtand in
need of; and at the fame time appointed two officers of his marine to meet
them and affift at their obſervations: one of theſe, Dom. Antonio de Ulloa,
on his return to Spain, publiſhed an accurate deſcription of the country,
which is tranſlated into Engliſh.
1199 In 1744 Bouguer read before the Academy an account of the expe-
dition
CHAP. IO.
495
ASTRONOMY
dition to Peru, whereof he printed a detail more at large in 4to in 1749ª:
the deſcription he gives of the country, the inhabitants, animals and vegeta-
bles is entertaining, but foreign to my purpoſe. There are near the equator
two ranges of mountains called las Cordilleras, fome of which are ſuppoſed
to be the higheſt upon the face of the earth: they ſtretch nearly from north
to ſouth about 170 leagues, having between them a vale 7 or 8 leagues in
breadth: in this vale they took their fundamental baſe of 6272 toiſes 4 feet
7 inches, conſtructed triangles, and placed ſignals which ſometimes were at
a great height, but were all reduced to the level of the fea: thus they mea-
ſured upon the meridian a length of 176940 toiſes, and, in order to find the
correſponding arc in the heaven that anſwered to this extent upon the earth,
and avoid all errors which might arife from aberration or any other motion the
ſtars might poffibly have, it was agreed in 1741 that Bouguer ſhould obferve
ſome ſtars near the zenith at one end of the meridian the fame night that Godin
obferved the ſame ſtars at the other: Bouguer obſerved at his end, but, Godin
failing to do his part, in the year following theſe fimultaneous obfervations were
made by Bouguer and Condamine: the refult was that they found the firſt de-
gree upon the meridian next to the equator to contain 56753 toifes: comparing
this with the mean degree as fettled by Caffini de Thury and the degree mea-
fured near the polar circle, Bouguer makes the polar diameter to be to the
equatoreal as 188 to 189. By § 1197, the ratio is as 168 to 169: by § 1194,
it is as 177 to 178; none of them very different from Sir Ifaac Newton's
computation, as 229 to 230: as note a, p. 492 ſhould be corrected.
1200 Bouguer, towards the end of his book fays he confidered that if, ac-
cording to the Newtonian philoſophy, every particle of matter attracts every
other particle, fo large a mafs of matter as fome of the vaft mountains of
Peru confift of, muſt have an attractive force; which, though ſmall, might
poffibly be diſcovered by its cauſing the plumbline to deviate a little out of
the perpendicular: in order to try the experiment, he went as near as he
could to what he judged to be the center of gravity of the Chimboraço, one
of the largeſt and, in appearance, of the greateſt folidity of the Cordilleras;
he was aware how inconfiderable the bulk of the largeſt mountain is in com-
pariſon of the whole globe, but then he could come fo much nearer to the
center of gravity of the Chimboraço than to the center of the earth, that by
a grofs calculation he concluded the attraction of that mountain would be
equal to about a 2000th part of the attraction of the earth: to fee if this were
fenfible, he took the diſtances of ſeveral ſtars from the zenith, at two diffe-
rent ſtations, one on the north, the other on the fouth fide of the mountain;
a La figure de la terre determinee par les obfervations de meffieurs Bouguer et de la Condamine, &c.
3 R2
and
496
BOOK 3.
ASTRONOMY
and, allowing for the distance between the two ftations, he found a difference
of 14" between the places of the fame ftars when viewed from the north and
their places when feen from the fouth ſtation: his obfervations were fo exact,
that he thought he had reaſon to attribute this deviation to the attraction of
the mountain, which drew the plummet 7 out of the perpendicular, to-
wards its center of gravity, that is, 7" towards the fouth when he was on the
the north fide, and 7" towards the north when on the fouth fide, fo as to
increaſe the diſtance between the apparent zeniths of the two ſtations 14″.
He would have tryed it on another very large mountain, but that had an-
other large one fo near it, that he imagined the attraction of one would'
counteract that of the other.
CHAP. II. SPOTS UPON THE SECONDARY PLANETS: THEIR ROTATIONS:
THE LIBRATIONS OF THE MOON.
}
1201 That the fatellits of jupiter are ſubject to have ſpots upon them has
been already mentioned, § 1105, 1121: there is alſo reaſon to conjecture
the fame of the fatellits of faturn, from what has been diſcovered of one of
them, namely, the fifth or outermoft: this fatellit, the revolution whereof
round its primary, is performed in about 80 days, had by Dom. Caffini
been obferved for feveral years, as it went through the eaſtern part of its
orbit, conſtantly to appear lefs and leſs, till it became quite inviſible; and
in the weſtern part to grow larger by degrees, till it arrived at its greateſt
brightneſs and magnitude ª.
a
}
1202 This phenomenon cannot be better accounted for than by ſuppoſing
one half of the furface of this fatellit to be unfit to reflect the light of the fun in
ſufficient quantity to make it vifible, and that it turns round its axis nearly.
in the fame time as it revolves in round its primary; and that, by means of
this rotation, and keeping always the fame face towards faturn, we upon
earth may, during one half of its periodical time, be able to fee fucceffively,
more and more of its bright fide; and during the other half of its period, have
more and more of the ſpotted or dark fide turned towards us. In the year
1705, this fatellit unexpectedly became vifible in all parts of its orbit, through
the fame teleſcopes that were before often made ufe of to view it in the
eaſtern part without fuccefsb: this fhews the ſpots upon this fatellit, like thofe
upon jupiter and fome other of the primary planets, are not permanent, but
fubject to change.
a Caffini, Mem. d'Acad. 1705,
b Maraldi, Mem. d'Acad. 1707.
1.
1203
CHAP. II.
497
ASTRONOMY
1203 Kepler thought the moon was carried round in her orbit by the rota- FIG.
tion of the earth, but denied the moon to have any rotation of her own; alledg-
ing for proof of this opinion, that fhe fhews us always the fame fpotsa: as he
held that the earth attracted the moon by a kind of magnetic force, it is
probable he imagined the greater denfity of that half of the moons globe which
is viſible to us, was the cauſe that tht fame half is always turned towards the
earth. To the bare eye, the ſpots of the moon always appear in the fame
form; but, by careful obfervations thereof with the teleſcope, it has been
found that this planet does indeed fhew us conſtantly the fame face nearly,
but not exactly: that the ſpots, continuing in the fame fituation in reſpect
of each other, appear fometimes to approach a little nearer to one edge of
the diſk, at other times to recede as much from the fame: this balancing
of the moon from one fide to the other, as if the center of gravity thereof
were changed, is therefore called a libration b.
1204 It is now known that the moon has a rotation round her own axis:
that this rotation is performed in the fame periodical time with her revolu-
tion round the earth: that during this revolution the axis of the moon con-
tinues always parallel to itſelf: that the axis of the moon is not perpen-
dicular to the ecliptic; though not greatly different from being fo: the
axis of the moon is elevated above the plane of her orbit 82 degrees and an
halfc.
The axis of the moon terminates always in the fame
points on the ſurface of that globe: the poles of the moon are therefore
fixed: the equator of the moon is alſo fixed, and paffes always through
the fame spots.
1205 As the moon turns round her own axis, in the fame periodical time
wherein the revolves round the earth and her axis is continually parallel to
itſelf, the fhews always the fame face to the inhabitants of the earth: this
is what appears to common fpectators, who think they fee always the fame
fpots; and this would really be the cafe, if the moon were carried round the
earth in a circle, and her rotation were performed round an axis always pa-
rallel to itſelf, in the fame periodical time as her revolution: in effect, the
orbit of the moon is an ellipfis, wherein the moves unequably round the earth
in one focus; the other focus is the center of the moons mean motion, to-
wards which ſhe always turns the fame face: hence it comes to paſs that
the moon is fubject to what is called her libration in longitude, that is, at one
time turns more of her eaſt fide, at another time more of her weft fide to-
wards the earth. In fig. 112, let the ellipfis ABCD repreſent the orbit of 112
a Kepler epit. aftronom. p. 556.
Hevel, felenograph, pag. 233,
b de libratione luna v. Gregorii aftronom. 1. 4. prop. 57.
c Caffini elements d'aftronomie. liv. 3. c. 3.
€
?
the
498
BOOK 3.
ASTRONOMY
FIG. the moon, wherein the goes, according to the order of the letters, round the
112 earth at the focus e; let the other focus be f, towards which, the moon
always turns what may be called her middle face, in reſpect of longitude,
as being in the middle between the two faces turned towards the earth in
her greateſt librations in longitude, one eastward and the other weftward:
when the moon is in apogee at a, her middle face is towards the earth at e;
for a ſtrait line drawn from the center of the moon to f will, if produced,
go to the center of the earth at e: as the moon goes from a towards b, more
of the eaſt ſide o is turned towards the earth, till at b ſhe ſhews the moſt of that
fide of her globe to the inhabitants of the earth that ever ſhe does; b there-
fore is the place of her greateſt eaſtern libration: from b this libration is
gradually diminiſhed to c the place of the moons perigee, where ſhe again
turns her middle face to the earth: from c fhe begins to turn her weft fide
towards the earth, and fhews us more and more thereof till fhe comes to d,
where ſhe is in her greateſt weſtern libration: from d this libration gradu-
ally leffens all the way to a, where the fhews again her middle face.
Thus we ſee that, with regard to eaſt and weſt, the moon fhews us her
middle face in apogee and perigee; and that her greateſt librations in lon-
gitude are at her mean diſtances.
As the moons apogee returns to the fame fituation, in refpect of the fun
and the earth in about 14 months, fhe goes in that time through all her li-
brations in longitude.
1206 As the axis of the moons rotation is inclined to the plane of her orbit,
and makes an angle therewith, in her revolution round the earth, the fhews us at
one time more of the northern part of her globe, at another time more of the
113 ſouthern part thereof; this is called her libration in latitude. In fig. 113, ABCD
is a perſpective view of the orbit of the moon, wherein fhe goes according to
the order of the letters, round the earth at e; when the moon is at A, the
turns towards the earth what we may call her middle face, in reſpect to her
libration in latitude; then her north pole n and her fouth pole s, are both in
the circumference of her diſk: when the moon is at B, her north pole n and
fome parts round the fame which could not be ſeen at A come into the vi-
fible difk; and her fouth pole with fome parts round it that were viſible at A
are hid from us: at c, we have again the middle face towards the earth: at
D the north pole n with fome parts round it that were vifible in the middle
face at c are hid from us; and the ſouth pole s with fome of the parts round
it which could not be ſeen at c, come into the viſible diſk.
1207 If we confider the ſpots of the moon as in fome meaſure repreſenting
an human face, we may ſay the libration in longitude turns at one time the
right
CHAP. 12.
499
ASTRONOMY
right cheek, at another time the left, towards the earth, fig. 112: and that FIG.
by the libration in latitude, we fee at one time more of the forehead, at ano- 112
ther more of the chin, fig. 113.
The moons libration in latitude turns her north and fouth parts towards
the earth alternately in a month, in the fame manner as the earth turns her
north and fouth parts towards the fun in a year.
There is alſo another change in the moons viſible face, improperly called
a libration, owing to the difference in her illumination by the fun: for, as
the enlightened parts only are vifible, the fame face turned towards the earth
may appear different, according as the moon is in north latitude, when the
fun enlightens her fouth pole and parts near it; or in fouth latitude, when
the fun ſhines upon the north pole and the parts round it. Greg. aft. b. 4 p. 58.
113
CHAP. 12. THE APPARENT MOTION OF THE SUN NOT EQUABLE:
THE NATURAL DAYS UNEQUAL: CLOCKS SOMETIMES FASTER
SOMETIMES SLOWER THAN THE SUN.
1208 Abfolute time or duration flows uniformly without any relation to
any part of the univerſe, and has from all eternity been the fame before the
exiſtence of any being, except that of the infinite Creator of all things who
never had beginning, and would for ever continue to flow on in the fame
tenor, if the whole creation were to be annihilated. According to Mr. Lockb
we meaſure the length of fmall portions of our time by the number of ideas
which ariſe fucceffively one after another in our minds: this I think muſt
be very different in different men: for, in the imaginations of fome they fol-
low one another with much greater rapidity than in thoſe of others; and the
fame man engaged in fome employment or amuſement that gives him
pleaſure thinks the hours much ſhorter than he would the fame length of
time if he were in pain or great uneafineſs of mind.
If we would with any exactneſs eſtimate the quantity of any portion of infi-
nite duration, or would convey an idea of the fame to others, we make uſe
of ſuch known meaſures as have been originally borrowed from the motions.
of the heavenly bodies; but eſpecially of thoſe luminaries the fun and moon,
which, among other ufes, were created to be for figns and ſeaſons, and for days,.
and years. It is true, the induſtry of aftronomers has difcovered that none of
a Grecis aswv,. Romanis evum; quod eft tempus unum et maximum, eſt enim immenfum, fine origine, fine:
fine, quod eodem modo femper fuit, et femper futurum eft Cenforinus de die natali, C... 16..
b Lock, of human underſtanding, book 2. chap. 14,
thefe
500
BOOK 3
ASTRONOMY
Y
theſe motions are exactly equable and uniform; but are ſubject to ſome ſmall
irregularities, which, though of no confequence in the affairs of civil life,
muſt be taken into the account, if we would find the places of the heavenly
bodies for any time paft or to come with any accuracy.
1209 We have already ſeen how irregular the motions of the planets and
comets are in their orbits; if there be any motion in nature perfectly equable
in the folar ſyſtem, it may be imagined the rotations of the fun and planets
round their own axes are fo; and yet, confidering the univerfal law of gra-
vity by which they attract one another, we cannot but own that if their
bodies are not throughout of an uniform denfity, which we are fure is not
the caſe of our earth, this muft occafion fome inequality in that motion,
though perhaps too fmall ever to be diſcovered. May not the rotation of
the earth be accelerated when the denfeft part of the fuperficies thereof is re-
volving towards the moon? is the interval of time between the tranfits of two
ſtars in the fame parallel always the fame, wherever the moons place be?
1210 The moſt obvious divifion of time is into day and night; theſe are
marked out by the rifing and ſetting of the fun: modern writers call the time
from funriſe to ſunſet the artificial day; the night is the time from ſunſet
to funrife: thefe days and nights are fubject to great inequalities in every
part of the earth except under the equator, as has been fhewn before. The
noſt ancient divifion of this day was into the morning and evening; the night
was divided into watches.
1211 What is now called the natural day a comprehends the day and night,
and is the time between the noon of any one day and the noon of the day imme-
diately following: this day is divided into 24 hours, every hour into 60 mi-
nutes, every minute into 60 feconds, &c: the beginning of it is different in
different countries; the Babylonians began the natural day at ſunriſe, the
Jews at funfet, as the Italians do alfo at this time: the Egyptians and anci-
ent Romans began the day at midnight, wherein they are followed by the
inhabitants of Great Britain and moft European nations: aftronomers general-
ly begin the day at noon, when the meridian of the place points at the fun.
1212 Hours are either equal or unequal: the equal hours have been juſt
now deſcribed: an unequal hour is the 12th part of an artificial day, or the
12th part of the night: in fummer when the days are the longeſt, the diur-
nal hours are the longeft, and the nocturnal hours fhorteft; in winter on the
contrary, when the days are fhorteft, the hours of the day are ſhorteft, and
a Aliter veteres; nam juxta Cenforinum, naturalis dies eft tempus ab oriente fole ad folis occafum, civilis
autem dies vocatur, tempus quod fit uno cœli circumactu quo dies verus et nox continetur: de die natali,
chap. 23.
b Cenforinus, ibid. v. ibi Lindenbrog.
c.Gregor. aftron. lib. 2. prop. 10.
thoſe
CHAP. 12.
501
ASTRONOMY
•
thoſe of the night longeft. The difference between the hours of the day and
thoſe of the night is greateſt at the folftices, becauſe then there is the greateſt
inequality between the length of the day and that of the night: at the equi-
noxes, when the days and nights are of equal length, all the hours both of
the days and nights are equal: for this reafon equal hours are by fome wri-
ters called equinoctial hoursa: unequal hours are fometimes called temporary
hoursb; either becauſe they are of different lengths at different times of the
year, or becauſe they were meaſured by ſmall portions which were called
Xgovor, times: one of theſe times appears to be four of our minutes, during
which one degree of the equator paffes through any meridian. Theſe times
might be meaſured by an aftronomer, but how unequal hours can be marked
out for common ufe is not eaſy to ſay.
The ancient Jews, Greeks and Romans, made uſe of unequal hours: with
them funriſe was the beginning of the first hour of the day, the third hour
ended about nine in the morning, noon was the end of the fixth hour, the
ninth hour ended about three in the afternoon, the twelfth at ſunſet: ſunriſe
was the end of the twelfth and laft hour of the night.
1213 Unequal hours are different at the fame time of the year in places of
different latitude: Ptolemy, in giving an account of fome ancient eclipſes that
had been obferved at Babylon, and ſet down in unequal hours and parts of
one of thoſe hours, reduces the times of them to equal hours and parts of an
equal hour, at Alexandria in Egypt, as a quarter, a third, an half, three-fifths,
&c. In thoſe paffages the latin tranflator for what in the original is half an
hour puts down 30 minutes, inſtead of three-fifths gives 36 minutes: this in-
deed expreffes the quantity fet down by the author by what is equivalent;
but may lead the reader into a falſe opinion that Ptolemy divided the hour
into minutes, which he does not appear to have done, though it be certain
he generally makes uſe of the fexagefimal divifion of a degree, as did alſo
fome more ancient writers.
1214 The ancients had fun-dials, but I think unequal hours could not be
marked thereon exactly: the only kind of clock made uſe of by them was the
clepſydra, which meaſured time by water running through a ſmall hole out
of one veffel into another: Vitruvius, 1. 9. c. 9. fhews how it might be fo
contrived as to mark out unequal hours at different times of the year. There
was a clepfydra in the famous court at Athens called Areopagus: the time mea-
fured by it was divided into three parts, whereof one part was allowed to the
plaintiff, one to the defendant, the third was for the judge; and there was an of-
a Ptolem. Almagest, 1. 2. c. 9. b Idem ibid. c Idem. 1. 1. c. 13. d 1. 4. c. 11. e Suidas diapeμgnan
nurga, ubi v. Kufterum. Clepfydram inter vafa et inftrumenta forenfia numer at Pollux, 1. 8. c 5. et l. 10. c 15.
3 S
ficer
διαμεμετρημένη
502
BOOK 3
ASTRONOMY
ficer appointed to take care that none of them exceeded his quota. If we had
fomething of this fort in our courts, it would greatly promote diſpatch of
bufinefs; but we ſhould often have the council copy a paffage in Demofthenes,
wherein he tells the court he had more to fay, but that he perceived the wa-
ter allowed him was almoſt run outa.
1215 The inequality of the natural days is now to be confidered, and the
cauſes thereof enquired into: if the fun were to appear all the year round
in the fame point of the ecliptic, for example, in the point r the interfecti-
on of the equator and ecliptic at the vernal equinox, the day would begin in
every place when the meridian of that place pointed at the fun in v, and end
when a compleat rotation of the earth brought the fame meridian to point
again at the fun in : if this were the cafe, the length of a natural day would
be no more than about 23 hours 56 minutes; for in that time, a rotation of the
earth is compleated, as appears by the following obfervation, any fixt ſtar
that is in the meridian at a given hour any night will, after 23 hours 56 mi-
nutes by a well regulated clock, be again in the meridian the night following:
this then is the length of what may be called a fydereal day.
1216 We have before ſeen that, by the annual revolution of the earth in
her orbit, the fun appears to go round in the ecliptic, according to the order
of the figns, § 642, this apparent motion of the fun is at the rate of about
one degree in a day: for he goes through the whole circle of 360 degrees in
a year, or 365 days 6 hours: if therefore any given meridian this moment
points at the fun in r, the rotation of the earth will in 23h 56′ bring that
meridian again to the point ; but in the mean time the fun will be
forward in the ecliptic about one degree, ſo that about 4 more muſt paſs be-
fore the meridian will again point at the fun, and compleat the day. The
time required over and above an entire rotation to compleat the natural day,
is not always the fame, but varies a little; it is fometimes more than 4,
fometimes lefs: this variation is owing to two cauſes, 1, the apparent mo-
tion of the fun being unequable, 2, the obliquity of the ecliptic.
got
1217 The unequable motion of the earth in her orbit, § 673, cauſes the ap-
parent motion of the fun in the ecliptic to be unequable; fo that he appears to go
fometimes more fometimes lefs in a day than 59′ 8″, which is his mean mo-
tion: the funs apparent motion is floweſt about the 30 of june new ſtyle, for
he is then in apogee in the 9th degree of: from thence his motion grows
ſwifter every day till about the 30 of december, when his motion is ſwifteſt,
and he is in perigee, in the 9th degree of : from thence his motion grows
continually flower, till he arrives again at his apogee, in the 9th degree of :
2 xaTA ETIQavov, prope finem.
κατα Στεφανον,
this
CHAP. 12.
503
ASTRONOMY
this difference in the velocity of the funs apparent motion caufes him to take FIG.
eight days more in going through the northern figns, from v to, than he
does in paffing through the fouthern figns, from to r; fo that our fum-
mer half year is eight days longer than the winter half year.
1218 If this cauſe were to operate alone, it is eaſy to ſee that the natural day
would be of the greateſt length when the fun is in perigee; for then his motion
is ſwifteft, and his daily step in the ecliptic is the longeft: and confequently
then the earth muſt continue turning the longeſt time after an entire rotation,
in order to bring the meridian of any place to the fun: on the other hand,
if this cauſe only were to operate, the ſhorteſt day would be when the fun
goes the floweſt, and makes the leaſt way in the ecliptic in a day: for then
a meridian turning round the fame way that the fun goes, would in the
ſhorteſt time come to point at him.
1219 The other cauſe of the inequality of the natural days is the celeſtial
equator and ecliptic cutting one another at oblique angles; if thofe circles
were coincident, that is, if the earths axis were perpendicular to her orbit,
fince all meridians are perpendicular to the equator, they would alſo be per-
pendicular to the ecliptic; and then, to compleat the natural day at any time,
the earth must turn round just as much more than an entire rotation as the
funs apparent motion in the ecliptic for that day amounts to: but this is not
the cafe: for, by reafon of the obliquity of the ecliptic, meridians cut
that circle at right angles only in the two folftitial points: in every other
part they make oblique angles with it, and more oblique ones the greater the
diſtance is from the folftitial points: and confequently they muſt fall upon
it with the greateſt obliquity at the equinoctial points and . From hence
it comes to paſs, that when the plane of any meridian continued, has gone
through an arc of the celeftial equator, fuppofe of one degree, it will not
have paffed through an arc of juſt the fame quantity in the ecliptic; but ge-
nerally more or less than a degree: more than a degree if the arc be taken
near the equinoxes. Fig. 117, is a view of part of the concave ſphere of
the heaven, wherein, let D E be a part of the celeſtial equator, F G a part of
the ecliptic, A the interfection of thoſe two circles at the vernal equinox,
A B a degree upon the equator; if we imagin the plane of the meridian to
paſs from the fituation M M into the fituation N N, in going through the arc
A B, one degree of the equator, it will go through the arc A C, which is
more than a degree in the ecliptic. For in the triangle ABC the angle at в is
a right one, confequently the hypotenufe AC is the longeft fide.
1220 At the folftices, the obliquity of the ecliptic has a quite contrary
effect, and helps to lengthen the natural days: this will eafily be compre-
hended
3 S 2
117
504
BOOK 3.
ASTRONOMY
FIG. hended by the 118 figure; where TT is part of the tropic of capricorn, CD
118 part of the ecliptic, which may be confidered as coincident with the tropic,
for ſome diſtance on each fide of the folftitial point, as from A to B ; and
therefore meridians which are perpendicular to the tropics, may be confider-
ed as perpendicular to the ecliptic, for that ſpace: this being ſuppoſed, a
meridian in going from A towards B, will go through as large an arc in the
tropic as in the ecliptic; but, the tropic not being a great circle, any arc as ab
taken in both thofe circles will meaſure more minutes in the tropic than in
the ecliptic, and that in the fame ratio as the ecliptic exceeds the tropic in
dimenfions: the circumference of the ecliptic is to that of the tropic nearly
as 60 to 55; and therefore the arc ab of 55 minutes in the ecliptic, will be
60 minutes in the tropic: now every meridian paffes in the fame time through
fimilar arcs in the celeſtial equator and all circles parallel to the equator, as
the tropics are: conſequently, at the ſolſtices, every arc of the ecliptic paffed
through by any meridian in a given time, will be to the arc of the equator
paffed through in the fame time as 55 to 60: at the fummer folftice, when
the fun is in the tropic of cancer, the earth being then near her aphelion,
where her motion in her orbit is floweſt, the funs apparent motion in the
ecliptic, during a natural day, is 57 12"; but the meridian of any place,
in order to país through 57′ 12″, in the ecliptic and compleat the day, muſt
go through 1° 2′ 24″ in the celestial equator: or to exprefs it more technically
the funs right afcenfion, at the ſummer folftice, changes 1° 2′ 24″, in a natural
day: now, as the time any given meridian paffes through the whole circle
of the equator is 23 hours 56 minutes 4 feconds, the time a meridian
takes in paffing through an arc of 1° 2′ 24″, muſt be about 4 minutes 9 fe-
conds, which added to 23 hours 56 minutes 4 feconds, the time of an entire
rotation of the earth gives the length of the natural day, at the ſummer ſol-
ftice, 24 hours 13 feconds.
1221 The fame reaſoning is applicable to the winter folftice, with this
difference that, the earth being then near her perihelion where her motion in
her orbit is ſwifteft, the funs apparent motion in the ecliptic is at the rate of
1° 1′ 10″ in a natural day; but, according to the ratio mentioned in the ſec-
tion immediately preceding, in order to paſs through 1° 1′ 10″ in the ecliptic,
a meridian muſt paſs through an arc of 1° 6′ 43″ in the celeftial equator; or
we may ſay the fun then changes his right aſcenſion 1° 6′ 43″ in a day: the
time a meridian takes up in going through this arc in the equator is 4 minutes
26 ſeconds, which added to 23 hours 56 minutes 4 feconds the time of the
rotation of the earth, brings out the length of the natural day, at the winter
folstice, 24
hours 30
feconds.
1222
CHAP. 12.
505
ASTRONOMY
1222 If we confider theſe two cauſes of the inequality of the natural
days, it appears 1, that the inequality of the funs apparent motion in the ecliptic
lengthens the days moft in december, and fhortens them moſt in june: 2,
that the obliquity of the ecliptic fhortens the days moſt in march and ſep-
tember, and lengthens them moft in december and june: 3, that the natural
days muſt therefore be longeſt in december, when both cauſes concur to length-
en them: 4, that in june the two caufes operate contrary ways, but the obliqui-
ty of the ecliptic lengthens the days more than the inequality of the funs
motion ſhortens them: 5, from the combination of theſe two cauſes the na--
tural day is ſhorteſt about the 15th of feptember, being then 23h 59′ 39″.
Corollary. The inequality of the natural day is the caufe that clocks or
watches are fometimes before fometimes behind the fun.
1223 A good clock well regulated goes uniformly on throughout the year,
fo as to mark the equal hours of the natural day of a mean length: a fun-
dial marks the hours of every day in ſuch a manner, that every hour is a 24th
part of the time between the noon of that day and the noon of the day im-
mediately following: the time meaſured by a clock is called equal time; that
meaſured by the fun-dial is apparent time. As the natural days meaſured by
the fun are unequal, the hours meaſured by the fun-dial muſt be alſo unequal,
that is, of different lengths, at different times of the year: the difference
between the length of the hours at different times of the year is ſo very ſmall,
that it may be quite neglected: the difference between the longeft natural-
day and the ſhorteſt, does not amount to fo much as one minute; the
greateſt difference between any two days immediately fubfequent is no more
than about one fecond; but this laſt difference, ſmall as it is, by being in the
courſe of ſeveral days accumulated, becomes confiderable. The mean natural
day is exactly 24 hours as meaſured by the clock.
fo
1224 The time of noon is feen by a common fun-dial; but more exactly
by a meridian teleſcope, that is, a teleſcope furniſhed with croſs hairs fo pla--
ced as to move in the plane of the meridian, to what ever angle it be ele--
vated: it is noon when the center of the fun is cut by the perpendicular hair,
and this is beſt ſeen through a ſmoaked glaſs, or by receiving the picture of
the fun through the teleſcope, upon a paper held in fuch a manner that the
light of the fun may fall perpendicular thereon.
In order to know by the ſtars whether a clock or watch keeps true time
or not, obferve the hour and minute when ſome ſtar is in the meridian, and
watch when the ſame ſtar is in the meridian again on the night immediately
following, if the clock then wants 3 minutes 56 feconds of the time of the firft.
obſervation, it goes well; otherwiſe it must be corrected. If a clock is to be:
examined
506
BOOK 3.
ASTRONOMY
examined by the fun, the beſt way is by a meridian teleſcope, as before de-
fcribed: if a fun-dial be made ufe of, the beſt time is at noon; for then, if
the dial be placed right, it will go true, though it be not made for the lati-
tude of the place where it is fixed. If a clock is to be ſet by a fun-dial, there
are but four days in the year whereon the fun-dial and the clock are together
at noon; namely, the 15th of april, the 16th of june, the 31st of auguſt, and
the 24th of december: on any other days if you would ſet a clock by the fun,
the equation table muſt be made uſe of, which ſhews for every day in the
year how many minutes or feconds the fun is before or behind the clock.
1225 The natural days are alternately lengthened and ſhortened: they
continue ſome time at the two extreams of longeſt and ſhorteſt, and afterwards
paſs gradually through their mean length from one extream to the other ex-
tream. When the natural days are ſhorter than 24 hours, the fun gains up-
on the clock; fo that if he be behind it he will get nearer to it, if he be with
the clock he will get before it, if he be before it he will get farther before:
on the other hand, when the natural days are longer than 24 hours, the fun
loſes with reſpect to the clock; ſo that if he be before it, he will grow leſs
before it, if with the clock he will get behind it, if he be behind it, he will
go on to be farther behind.
1226 Between the winter folftice and the funs being in perigee, when both
the cauſes before mentioned confpire to lengthen the natural days, they are at
the longeſt, and continue for fome time of the fame length, exceedingly near,
each day being 24 hours 30 feconds long; and therefore, though the fun is
with the clock on the 24th of december, on the following day the 25th, as
the clock goes round in 24 hours exactly, the fun will be 30 feconds behind
it, on the 26th one minute, on the 27th 1′ 30″ behind the clock, lofing 30
ſeconds every day, ſo long as the natural days continue of the fame length
of 24h o 30": and when they fhorten, the fun will continue lofing, though
every day lefs and lefs, till the 10th of february, when all thoſe lofings ac-
cumulated together will bring the fun behind the clock 14′ 43″, which is the
moſt he is ever behind it: for the natural days being then, by gradually ſhort-
ening, come to their mean length of 24 hours, and continuing to fhorten
near a fecond every day, the next day will be only 23h 59′ 59″ long, the
day following 23h 59′ 58″ long, and fo on; wherefore the fun then going
round every day in leſs than 24 hours, will begin to gain upon the clock, ſo
as to get every day nearer and nearer to it, thoſe daily gettings being more
and more as the days fhorten, till the 15th of april, when the fun having got-
ten all he had loft before, will now go again with the clock; but the natu-
ral days though fomething longer than they were the latter end of march,
J
being
CHAP. 12.
507
ASTRONOMY
being fill feveral feconds lefs than 24 hours, the fun will continue to gain
upon the clock and confequently get before it; and this gain, though leſs and
leſs every day as the days lengthen, will be accumulated till the 15th of may,
when the natural days are again of their mean length, the fun being then 4′ 4″
before the clock: from that time the natural days increafing to be more than
24 hours long, the fun will begin again to loſe in reſpect of the clock, though
at firſt but one ſecond in a day, and will by the farther increaſe of the natu-
ral days go on loſing more and more every day; fo that by the 16th of june
the fun will have loft all he had gotten before the clock, and they will again.
go together: but this coincidence will not continue, for the natural days,
though not fo long as in december, are now feveral ſeconds more than 24
hours long, and continue a confiderable time of the fame length; ſo that the
fun will the next day be behind the clock, and will continue lofing about
13 feconds in a day at firſt, but every day leſs and lefs as the natural days fhor-
ten, till they again become of their mean length, about the 26th of july;
when the fun will have loft 5′ 55″ of the clock: from this time the natural
days continuing to grow fhorter, will be each of them leſs than 24 hours;
fo that the fun will begin to gain upon the clock, and will be every day leſs
and lefs behind it until he has gotten all the 5′ 55 up again, which will hap-
pen about the laft day of auguft, when he will be with the clock, and the
days ſtill ſhortening, the fun will get before the clock, and gain daily more
and more upon it till about the middle of ſeptember, when the natural days
are at the ſhorteft of all; and though the daily gettings are afterwards lefs
and lefs, they will be fo accumulated that the fun will be 16′ 9″ before the
clock by the beginning of november, when the natural days are fo increaſed
as to be of their mean length: from this time the natural days growing lon-
ger
than 24
24 hours, the fun will begin to loſe, and go on lofing every day more
and more till thoſe days are again at the longeft, about the 24th of december,
when the fun and clock will again both fhew the fame time.
1227 The following table is taken out of the Conoiffance du temps for the
year 1752, and will ſerve very well for the reſt of the prefent century; the uſe
of it has been mentioned § 1224; an example or two will make it eafy to be
underſtood. If I would fet the clock by the fun at noon on the 5th of january,
I muſt ſet it at 6′ 4″ paſt 12; for ſo much is the fun then behind the clock:
again, on the 10th of june, the fun is 1′ 12″ before the clock; ſo much on that
day ſhould the clock want of 12 when it is noon by the fun.
Domenico Caffini made the firſt table of this fort in 1668, it is printed
among his tables of the fatellits of jupiter, and in the Philofophical tranfacti-
ons n. 214, and did well enough for the reſt of that century.
A TABLE
508
BOOK 3.
ASTRONOMY
Days |
"
"
"
"
I
4 14 14 9 12 423
57 3
92
A TABLE OF THE EQUATION OF TIME; SHEWING HOW MUCH THE SUN IS
BEFORE OR BEHIND THE CLOCK EVERY DAY IN THE YEAR, New Style.
Jan. Feb. March April May June July Aug. Sept. Oct.
Sept. Oct. Nov. Dec.
Obehind Obehind Obehind Obehind Obefore before Obehind Obehind
"
Obefore Obefore Obefore Obefore
"
"/
"
9 10 28
45 3 10 5 46
0
2 4 42 14 16 12
29 3
38 3
17 2
36 3 21 5 42
18 10 21 16
0 36 10 40 16
3
5 10 14 22 12
16 3
20 3
24 2
26 3
32 5 38
0
55 10 58 16
910 5
91 9 41
4 5 37 14 27 12
313
23
31 2
17 3
43 5 33
I 14 11 16 16
8 9 17
6
414 32 11
492 44 3
36 2
7 3
54 5 28
1 34 11 34 16
6
68
8 52
6 30 14 36 11
352 26 3
411
57 4
4
45 22
I
1 53 11 51 16
6 56 14 39 11
20 2
93
461
46 4
145 15
2 13 12 816
38 26
8
O
8 7 2114 4111
51
52 3
50 I
35 4 24 5
8
2 33 12 24 15 55
7 34
9 7 46 14 43 10
501
35 3
54 1
24 4 33 5 O
2 53 12 40 15 50
7 7
IO
8 11 14 43 10
34 1
18 3
57 1
12 4 42 4 52
3
14 12 56 15 44
6 39
I I 8 35 14 43 10
181
13
591
04 504 43
3 34 13 1115 37
6 12
12
8.58 14 42 10
10 45 4
Io
48 4
58 4 34
3 55 13
25 15 29
5 43
13 2014 419
9 20 14 41 9
440 29 4
30
36 5
5
5 4 24
5 4 24
4 16 13
40 15 21
5 15
14 9 42 14 38 9
270 13 4
40
24 5
24 5
12 4 13
12 4 13
4 36 13
53 15 12
4 46
1510 314 35 9 100 24
Obefore
40,115 194 2
4 57 14
615 I
4 17
Obehind
16 10 24 14 31
8
520 17 4
17 4
40
40 25 25 3 5
5 18
5 18 14
19 14 50 3 48
17 10 44 14 27
8
340 31 4
340 31 4
30 14 5 30 3 38
5 39 14 3114 38 3
3 18
18 11 3 14 22
8
160 45 4
19 11 21 14 16
7
580 593
II
9
20 11 39 14
2111 56 14
2 7 221 26 3 53 I
22 12 12 13 54 7 3 31
23 12 27 13 456 451
24 12 42 13 36 6 26 2 2 3 411
2512 56 13 26 82 13 3 351
5 492 243
26 13 8 13 16
27 13 20 13
28 13 32 12 54
5
6
7 40 1 13 3
10
IO 27 5 35 3 26
590 40 5 40 3 13
570 53 5 44 2 59
65 472 45
245
38 3 50 1 19 5 50 2 30
50 3 46 1 325 52 2 15
32 5 52 2 15
44 5 54 2 O
57 5 551 44
6
0 14 42 14 25 2 48
6
20 14 52 14 12
2 19
6 4115 313 57
I 49
215 12 13 42
7
7 22 15 21 13 26 0 49
7 43 15 29 13
O 19
Obehind
Ο ΙΙ
8 315 36 12 52
8 24 15 43 12 33 0 41
I 19
9
29 2
f
29 13 42
30 13 52
3114 I
5 302 34 3
5 112 44 3
4 532 533
4343
4 15
23 2
I 13
9 5 551 28
95
225 551 II 9 415 54 11 54
16 2 34 5 550 54 9 23 15
92 2 46 5 540 37 9 43 16
12 58 5 520 19 10 2 16
8 44 15 49 12 14
I II
I 41
58 11 34
2 10
211 13
2 40
510 51
3 9
2 53
5 4910 I
16 7
3 38
CHAP. 12.
509
ASTRONOMY
In the common equation tables it is ſometimes faid the clock is too faſt or
too flow; this is not true, for a good clock goes always alike and keeps equal
time: fometimes they put it down that the fun is fafter or flower than the clock;
this may lead into a miſtaken opinion, that every day of the year meaſured by
the fun is ſo much longer or ſhorter than the ſame meaſured by the clock as
the reſpective equation amounts to: this is not the cafe; for, when the fun
has got confiderably before the clock, he may, after loſing ſo much of his
motion, abfolutely ſpeaking, as brings him to equal time, be ftill before the
clock: in like manner, he may be behind the clock on a day which meaſu-
red by his motion is equal to or even ſhorter than the day meaſured by the
clock; becauſe he has not yet gained enough of what he had loft to bring him
even with the clock: for this reaſon I choſe rather to ſay the fun is before or
behind the clock.
By the equation table apparent time may be reduced to equal, or equal
time to apparent: thus, march the 5th the fun is 11′ 49″ behind the clock;
fo much then muſt be added to the apparent to bring it to equal time, or ſo
much muſt be taken from equal time to reduce it to apparent. In comput-
ing the motions of the heavenly bodies, we make uſe of equal time; but in
fetting down the time when any appearance in the heaven will happen, we
expreſs it in apparent time, becauſe that is of more general uſe.
Remarks upon CHAP. 12. § 1214.
1228 The fun-dials of the ancients to fhew the unequal hours were not
made in the method uſed at preſent, with a gnomon parallel to the axis of the
earth, as deſcribed § 324; but had a pin ſet upright upon a plane and rounded
at the upper end into a globe, the ſhadow whereof marked their unequal
hours in the following manner: by means of an analemma or projection of
the ſphere, fix curves were drawn upon the plane to fhew where the ſhadow
of the pin at the ſeveral hours of the day terminated, every month in the year:
one curve ferved for two months, becauſe the ſhadows are of the fame length
in january as in december, in february as in november, în march as in october,
&c: each curve was drawn long enough to take in all the hours of the longeſt
day in the reſpective months, and was divided into twelve equal parts: it is ea-
ſy to ſee that a dial made by this method, in order to fhew the unequal hours
exactly, ought to have half as many curves as there are days in the year;
but this would require fo many lines as would make it all confuſion: it is
probable they had only one line for a month, and that for the middle of the
month.
3 T
Palladius
510
BOOK 3
ASTRONOMY.
1229 Palladius, an ancient Roman writer upon agriculture, having fet
down what is the proper work to be done in the farm or the garden, each
month in the year, gives the length of the ſhadow for every hour of the day,
as in the following example of the month of april.
The hours in this month are of the fame length as the hours in feptember.
Of the bours.
ΙΟ
7
the first hour
[24
fecond
14
third
fourth
fifth
fixth
is
4
feventh
eighth
ninth
tenth
5
7
IO
14
eleventh j 24j
feet
The uſe of this feems to be that the labourers
might gueſs at the time of the day by the length
of the fhadow: it is rightly fuppofed by Salma-
fusa, that the author meant the labourer ſhould
find the time from the ſhadow of his own perfon:
the rule, fuch as it is, will hold good in men of
different flature; becaufe, generally fpeaking,
the length of a mans foot bears nearly the fame
proportion to his height, whether he be tall or
middle fized.
1230 The clepfydra is pretty well defcribed by Vitruvius b. In Perault's
French tranſlation of that author, there are elegant cuts of the clepſydra:
but no body I fuppofe will now think of making one, as clocks and watches
meaſure time fo much better. I do not find hourglaffes of fand to have been
of very ancient ufe. Tycho Brahe had ſeveral clocks that fhewed the hours
minutes and feconds, which he ſays were made in the beſt manner (the
regulating clocks by pendulums was not found out till many years after )
but not being able to meaſure time ſo exactly with them as he was defirous
to do, he made uſe of hourglaffes, fome filled with quickfilver well purified
by diſtillation which was let to run through a very ſmall hole of metal, others
with lead calcined and reduced into a fine powder; but neither of thoſe ex-
periments fucceeded to his fatisfaction c.
>
CHAP. 13. WEEKS, MONTHS, YEARS, PERIODS OR CYCLES,
1231 The divifion of time into weeks was by divine appointment, and
is as ancient as the creation of the world, as appears by the facred writings,
Gen. c. 2. v. 3. the week of 7 days was always in ufe among the Jews, and is
univerfally received by Chriftians of all nations, and by the Mahometans in
all countries: Scaligerd fays it has been in uſe among all the people of the eaſt
c Progymnaſmat. p. 150.
a Plinian. exercitat.
b 1.9.c.9
à de emendat. temp. p. 9.
from
CHAP. 13.
511
ASTRONOMY
T
from the moſt ancient time: this was probably owing to ancient tradition:
the cuſtom of giving names to the days of the week from the fun moon and
planets, as an hiſtorian who lived in the fecond century tells us, came ori-
ginally from the Egyptians, and was by them propagated among other na-
tions: he fays the Romans in his time followed it, but the Greeks did not,
as far as he knew a. Our anceſtors the Saxons, before their converfion to the
Chriſtian faith, named the ſeven days of the week from the fun and moon
and fome of their deifyed heroes, which names we received with the rest of
their language and ftill retain: funday was devoted to the Sun, monday to
the Moon, tuesday to Tuifco, wedneſday to Woden, thursday to Thor, friday
to Friga, faturday to Seaterb. Some of our fectaries fcruple making uſe of
theſe names upon account of their owing their original to idolatry, not
confidering that names or words are of themſelves indifferent, and can only
become bad where they convey or excite vicious ideas. What was very foon
after the reſurrection of our Bleffed Saviour called the Lords day, was after-
wards called the day of the fun or funday by fome of the ancient fathers,
who detefted the idolatry of worſhipping the fun as much as any body now
can doc: but they spoke the language then in uſe, as the facred writer alfo
did, when he called the place of judicature at Athens by the name it com-
monly went by, Areopagus or Mars-hill d.
1232 The month has its name in ours and ſome other languages from the
the moon, and is the time of a revolution of that planet round our earth: the
month is periodical or fynodical, as has been mentioned § 958 and 959: the
fynodical confifts of about 29 days and an half, and is of moft general uſe,
as it is the time wherein the moon goes through all her phaſes, whereby we are
able to know at what hours of the night we may expect the benefit of moon
light; as alſo to foretell the time of high and low water, at all places where
the tide ebbs and flows.
1233 A year is the time wherein our earth revolves in her orbit round the
fun: the year as confidered by aftronomers is either fydereal or tropical: the
fydereal year confifts of 365 days 6 hours and 10 minutes, in this time the
earth revolves round the fun, and makes the fun appear, after having been
in conjunction with ſome ſtar, to go round the ecliptic, and come again into
conjunction with the fame ftar: the tropical year is the time wherein the fun,
after appearing in one of the cardinal points, goes round in the ecliptic till
he comes again to the fame point: the tropical year is about 21 minutes in
time ſhorter than the fydereal: becauſe the cardinal points go backwards
b Verftegan, antiquities of the Engliſh nation,
d Acts. chap. 17. v. 19 & 22.-
a' Dion Caffius. hift. I. 37. pag. 42. edit. H. Steph.
chap. 3 ·
c Juttin Martyr. apol. 2.
3 T2
every
512
BOOK 3.
ASTRONOMY
every year about 50 feconds of a degree, § 657 and 781, and meet the fun
fo far in his apparent annual progreſs through the ecliptic.
1234 The time a planet takes in revolving round the fun, is ſometimes
called the year of that planet: thus, about 7 months may be faid to be the year
of venus, about 3 months the year of mercury, &c. The going back of the
cardinal points juſt now mentioned, was thought by the ancients to be owing
to a flow motion of the ſphere of the fixt ftars round the poles of the ecliptic,
contrary to the order of the figns: fome of them imagined an entire revolu-
tion of the ſphere would bring about a renovation of the world, and reſtore
every thing into the fame ſtate and condition as at the beginning; this period
was therefore called magnus annus the great year, and mundanus annusª the
year of the world: the length of it was variouſly affigned by different phi--
lofophersb: if they had known how much the yearly preceffion of the equi-
nox amounts to as well as the aftronomers of the preſent age do, they would
have ſettled the length of the annus magnus at 25000 years. If we confider
that the preceffion of the equinox is owing purely to the change of the fitu-
ation of the equator and poles of the earth, cauſed by the attraction of the
fun and moon, eſpecially the laft mentioned of thofe luminaries, the fpe-
culation concerning the great year will appear to be of very little confe-
quence.
1235 The civil or political year has a different beginning, and is of a diffe-
rent form in different nations: the ancient Egyptians made uſe of the folar
year pointed out by the apparent annual motion of the fun; to this they al-
lotted 360 days, and divided it into 12 parts or months, each month containing
30 days: (here we fee the origin of the divifion of the ecliptic and other cir-
cles into 360 parts, and of the zodiac into 12 figns:) the redundant 5 days
were thought not to belong to the year, and therefore no bufinefs was to be
done upon thoſe days, but they were ſpent in idleness and diverfion: they
were afterwards dedicated to five of their deities; and in fine received into
the year, but were added to the end of it, and were called ɛayoμevat or
additional: this year of 365 days their Kings took an oath in the temple of Ifis
not to change by intercalation, and is the year meant by aftronomers, when
they compute by Egyptian years: fome writers fay that their year took in
not only the 365 days, but the redundant fix hours alfo: and indeed it feems
utterly improbable that their Hierophante who had the care of theſe affairs
and were ſo knowing in aftronomy, ſhould be ignorant that fix hours or nearly
that quantity of time was neceffary to meaſure the annual motion of the ſun
or of a ftar: why this piece of a day was omitted in their common year of
a Macrob.fomn. Scip. 1. 2. c. 11I.
b Cenforinus de die natali, c. 18.
365
CHAP. 13.
513
ASTRONOMY
cc
<<
365 days, we may learn from an excellent Greek author, who according to
Petavius, lived in the time of Sylla: "The Egyptians (fays he ) did not
"take the quarter of a day into their account, that their facred feſtivals might
go forward, as they would do by this omiffion, one day in four years, ten
days in forty, a month in an hundred and twenty, fo as to go through all
"the ſeaſons of the year in 1460 years; whereas the Greeks by their laws
"and by an oracle were directed to keep their facred folemnities in the ſame
"months in the year, and on the fame days of the months; for which pur-
"poſe, they made ute of intercalations, to bring the accounts of the motions
"of the fun and moon as near together as poffible. The beginning
of the Egyptian year was originally, at the heliacal rifing of the dog ſtar,
to which they paid divine honours, probably becauſe at that time the Nile
began to rife, upon the overflowing whereof the fertility of their country
greatly depends.
>>
1236 The month made ufe of by Mofes was of 30 days, as appears from
theſe paffages, on the 17th of the 2ª month the rains began which brought on
the deluge, gen. c. 7 v. 11; on the 17th of the 7th month the flood was fo far
abated that the ark reſted upon mount Ararat, gen. c. 8 v. 4: now from the
7th of the 2d month to the 17th of the 7th month, allowing 30 days to each
month, is juſt 150 days, the number of days the waters are faid to have
prevailed upon the earth, gen. c. 7. v. 24. and c. 8. v. 3:
1237 There is in Whiston's Theory of the earth, a learned differtation,
wherein it is fhewn that in very ancient times various nations had the fame
year with the Egyptians of 360 days, and the month of 30; that this can no
way be fo well accounted for as by fuppofing that the year and month were
exactly of that length before the flood; and that (mankind being generally te-
nacious of old cuſtoms, though found inconvenient) the fame meaſures of time
continued to be retained even after they were difcovered not to agree with
the motions of either the fun or the moon: it is alſo conjectured that the al-
teration of the year from 360 to 365 days and a quarter was owing to a co-
met, which in its near approach to the earth, by diſcharging thereon a great
quantity of vapours from its atmoſphere, and breaking the external cruft and
forcing up the waters of the great abyſs, brought on the flood; and did alſo,
by the acceffion of new matter, diminiſh the velocity of the diurnal motion
of the earth; and, by attraction or gravitation, turned her annual orbit from
a perfect circle into an ellipfis.
•
1238 The lunar year conſiſts of 12 fynodical months or lunations: 12 of
theſe months amount to 354 days, and come the neareſt of any number of
a..Geminus, cap, 6, de mensibus.
b. p. 144. 4th edition, 1725.
months
514
BOOK 3.
ASTRONOMY
months to the length of a folar year, but fall fhort of it 11 days: this year is in
uſe among the Turks and other Mahometans: the beginning of it goes back II
days every year, which, every 8 years fets it back 3 months; fo that if the
beginning of the prefent year were in the fpring, 8 years hence it would be
in the winter, 16 years hence in the autumn, after 24 years in the fummer,
after 32 years in the ſpring again: this is called a wandering year, becauſe
the beginning of it runs through all the feaſons in half the period of the life
of man.
1239 The ancient Jews and Greeks made uſe of what may be called a
lunifolar year, wherein they adjuſted the lunar and folar year fo as to bring
them as near as they could, to the fame beginning: for this purpoſe they
invented feveral ways of intercalating or inſerting days into the lunar year:
one ſcheme was the octennial period, which the Jews intercalated in the fol-
lowing manner: they found that the excess of the folar above the lunar year,
being about 11 days and a quarter, in 8 years amounts to 90 days, that is 3
months of 30 days each: they therefore added one of theſe months at the end
of the 2d year, another at the end of the 4th, and the 3d at the end of the 7th
year; fo
ſo that each of theſe years the 24, 4th, and 7th, confiſted of
13 months:
they did not give a new name to the intercalated month; but, as the name of
the laſt month of the jewiſh year was adar, they called the additional month
veadar, as much as to fay another or a fecond adar. The beginning of the
ancient Jewiſh year was at the autumnal equinox; but after their going out
of Egypt the beginning of their year was at the vernal equinox.
1240 The ancient Greeks were commanded by an oracle to obſerve, in
their facrifices, the cuſtom of their country, in three particulars; theſe were
underſtood to mean days, months, and yearsa: many of their feftivities as well
facred as civil, were celebrated at the new or full moon which fell out near one
of the folftices or equinoxes; in like manner as the Jews were to keep the
paffover on the full moon next after the vernal equinox: their aftronomers
therefore endeavoured to find out a cycle or period, wherein the fun, having
run through a number of compleat years, and the moon a number of compleat
fynodical months, thofe luminaries would begin again to go through a like
number of years and months, in the fame manenr as before. They made
uſe of the octennial period, but are faid to have intercalated the months at
the end of the 3d, 5th, and 8th years.
1241 As aftronomy made now fome progrefs among the Greeks, the octen-
nial period was found to be defective; whereupon Meton an Athenian, invented
the period of 19 years, which was thought to contain exactly 6940 days, or›
235 fynodical months; that is, allotting 12 months to each of the 19 years,
a Geminis ubi fupra. Scalig. de emendat, temp. p. 36.
7 fuper-
CHAP. 13.
515
ASTRONOMY
7 fupernumerary months, which were to be intercalated at the end of the 24,
5th, 8th, 10th, 13th, 16th and 18th year: but, as aftronomy continued ftill to
improve, it was found that 6940 days exceeded 19 folar years by at leaſt à
quarter of a day, and 235 lunations by fomething more: fo that the new
moon at the end of that period would anticipate the time of the new moon
at the beginning thereof: to remedy this, Calippus having quadrupled the
6940 days of Meton, and taken out of the fum arifing therefrom one day, in
order to account for the excess of the 4 quarters of a day, publiſhed his pe-
riod of 27759′ days; which amount exactly to 76 Julian years: this period
long obtained among the Greeks, as it kept both the ſeaſons of the year and
the new moons nearer to the true times than the period of Meton would have
done: but when the correction of the Roman year by Julius Cæfar pre-
vailed, the period of 19 years was again brought into ufe; and, becauſe it
was imagined that after the completion of 19 Julian years, in every ſubſe-
quent period the new and full moons would fall out on the fame days, this
period is often called the cycle of the moon.
1242 The ancient Roman year has by fome authors been faid to have
confifted of no more than ten months: the ground of this affertion feems to
be that march was the firſt month of their year, and ſeveral other months had
their names from the order in which they followed; thus, the ſeventh month
from march was called feptember, the eighth october, the ninth november,
and becauſe the numeral names proceeded no farther than december, that
was concluded to be the laſt month: whereas feveral authors expreffly ſay
that the year ended with january and february, and that theſe two months
were afterwards in the time of Numa, or later than that, removed from
the end to the beginning of the year, where they now ſtand.
As this year of the Romans was lunar; in order to make it fo far agree
with the annual courfe of the fun that the beginning of it might in fome
meaſure be fixed, fo that the beginnings of the four ſeaſons might fall out in
the fame months, they made ufe of an intercalation, but fomething different
from thoſe juſt now mentioned: for, the deficiency of the lunar year from the
folar being about II days and a quarter, the double whereof is 22 days and
an half, they every other year intercalated, between the twenty third and
twenty fourth of february, a fhort month, which they made alternately of 22
or 23 days: the care of intercalating was committed to the prieſts, who are
faid by negligence and corruption to have suffered the year to go into fuch
diforder, that their facrifices and feſtivals were by degrees run out of the
per ſeaſons.
a Geminus, c. 6. Ptol. 7. 3. c. 2. b v. authores in Grævii Thefaur Roman ant, vol. 8.¸
pro-
1243
516
BOOK 3.
ASTRONOMY
1243 Julius Cæfar, having been ſome time in Egypt, brought from thence
Sofigenes, who affifted him in correcting the Roman year, and reducing it to a
nearer correſpondence with the motion of the fun: for, whereas the Egyp-
tian year of 360 days, with the additional five added by them at the end there-
of, falls ſhort of the true tropical year about fix hours, which quarter of a day
cannot well be put into the calendar, he ordered that, every fourth year, the
elapfed quarters of a day ſhould be accounted for, by inferting for them one
whole day between the 23d and 24th of february, the ancient place of inter-
calation: and, becauſe the 23d of february in the Roman calendar was called
fexto calendas martii, the fixth of the calends of march, the intercalated day
was to be called bis fexto calendas martii, the fecond fixth of the calends of
march, from whence the year of intercalation had the appellation of biſſextile.
1244 The Julian year, as corrected by Auguftus Cafar after being again
in diforder by the miſmanagement of thoſe who had the care of the inter-
calation, was eafily introduced into all civilized nations who fubmitted to the
Roman power; and continued in general uſe till the year 1582, when Pope
Gregory the thirteenth reformed the calendar, and brought in what was from
him called the Gregorian year: this Pope who was a learned man and had
been proffeffor at Bononia, thinking it was of importance to the authority of
the holy ſee that he ſhould have the fole direction of the affair; to make it
go down the more eafily, fent the ſcheme of the intended alteration drawn
up in a ſhort treatiſe by Aloyfius Lilius to feveral courts of the Chriftian
Princes, and to the moſt confiderable univerſities: and in the year 1582 pub-
liſhed a bull commanding the obſervation thereof: it met with great oppo-
fition among the Proteftant ftates; and, when received by fome of them, it
was with a falvo that it ſhould not be underſtood as a fubmiffion to the Papal
authority a: the intent of this correction of the year was to bring back the fef
tivals of the church to the fame days of the month, and the months to the
fame ſeaſons of the year as they were in at the time of the council of Nice,
held A. D 325, when the time of keeping Eaſter, which had been the oc-
caſion of great diſturbances in the Chriſtian world, was finally determined.
1245 There was ſome difference among the ancients in their opinions about
the exact length of the tropical year, as may be ſeen in Ptolemy, l. 3. c. 2.
Hipparchus, by comparing his own obfervations with fome more ancient
ones, concluded it to be 365 days 5 hours 55 minutes: later aſtronomers,
by being able to meaſure longer periods of years, have determined it at about
6 minutes leſs; by all accounts it appears that one day is too much to be in-
tercalated every four years; fuch intercalation caufes the times of the funs
2 v. Thuani, biſtor. fui. temporis, 1. 76 pag. 11. edit. Lond. et. Munkerum, de intercalatione.
arrival
CHAP. 13.
517
ASTRONOMY
arrival at the cardinal points to fall out every year eleven minutes earlier
than by the Julian account they ought to do: this anticipation of eleven mi-
nutes in a year amounts in 130 years to a whole day: hence it came to pafs
that the vernal equinox, which at the time of the council of Nice fell out
on the 21st of march, was in the the year 1582 advanced forward to the
IIth of march: to rectify this, the bull ordered 10 days between the 4th and
15th of october in that year to be fuppreffed, ſo that the day which in the
Julian account would have been the 5th of october was to be called the 15th:
and, that the vernal equinox thus reſtored to the 21st of march might not
deviate out of its place for the future, the intercalation of a day in february
every fourth year was to be continued as formerly, except the hundredth
years now to be mentioned: the year 1600 was to be biffextile; but in every
400 years after that, three intercalary days were to be omitted: that is to fay,
in the laſt year of the firſt ſecond and third century, there ſhould be no in-
tercalation; but the laſt year of the fourth century ſhould be biffextile: fo
that for example, the years 1700, 1800, and 1900 ſhould not be biffextile;
but the year 2000 fhould: and that this order of intercalating fhould be ob-
ſerved through every 400 years for ever. This correction does not entirely
remove the error; for the cardinal points ſtill anticipate near two hours in
every 400 Gregorian years, but this defect is quite inconfiderable; for it
does not amount to above one day in 5000 years. See phil. tranfact. n. 495-
1246 In the year 1752, the Gregorian year or new style, was by act of
parliament enjoyned to be received in Great Britain, and all the Britiſh do-
minions; and the dates of all deeds and other writings to be made accord-
ing to the new ſtyle, whereas before that time they were all dated according
to the Julian year or old ftyle. As above a century was then paft fince the
Gregorian correction, in which time the cardinal points had anticipated one
day more, eleven days were fuppreffed in the new Britiſh calendar: this was
done by ordering the third of feptember to be called the fourteenth. By the
fame act, the legal beginning of the year was changed from the twenty fifth
of march to the firft of january.
The year being now ſettled, we may refume the confideration of months,
weeks and days, in order to underſtand the nature of the calendars or alma-
nacks of the ancients and moderns, and the rules for finding Eafter.
ક
1247 The ancient Greeks divided each month into three parts or decads;
the firſt decad was called the beginning of the month, the ſecond the middle,
the third the laſt of the month. The first day of the month was called 8-
δευτερα ισαμεν,
the new moon; the fecond deutega 15aμev8, the ſecond inſtant; the
TOITY 15 aμere, the third inſtant; and fo on to the tenth, which was
3 Մ
μενια,
third
τρίτη
called
518
воок 3
ASTRONOMY
called δεκατη ιςαμεν8 the tenth inftant: the eleventh was called πρώτη μεσεντος,
the firſt of the middle, or #gwn ε dena, the firſt after the tenth; the twelfth
δεύτερα μεσεντος, the fecond of the middle, or δεύτερα ETTI dexa, the fecond af-
ter the tenth; and fo on to the twentieth, called eixas or emos: the twenty
εικας eixo5n:
firſt was called Owl ETT Emad, the firft after the twentieth, &c: in this laft
decad the moon was fo much in the wain that they gave it a name from a
word that fignifies to decay or periſh; and, reckoning the days backwards
from the laſt day of the month, called the twenty firſt day denalʼn plwortos,
the tenth of the waining or the tenth from the diſappearing moon, if the
month confifted of 30 days; or evval volos, the ninth of the waining, if
the month confifted of 29 days: the twenty fecond day was called evval -
εννά η φθι
volos, the ninth of the waining, in the former cafe, and oydon polos, the
eighth of the waining in the latter; and fo on to the day before the laſt,
which was called delega polos, the ſecond of the waining: the laſt day of
the month, whether it were the twenty ninth or thirtieth, was called evŋ »
मझे
Vea, the old and new; as it partook of the old and new moon. a The names
of the first and laft decads are as ancient as Homerb.
νεα,
ενη
1248 The Romans divided their month into calends, nones and ides, they
reckoned all of them backwards as the Greeks did the laft decad: the firſt
day of every month was called calenda, the calends of that month, the laſt day
of every month was called pridie calendas, the day before the calends of the
month following &c: thus, the 30th of april was called pridie calendas maij,
the day before the calends of may; the 29th of april, the 3d before the ca-
lends of may; the 28th, the 4th before the calends of may; and fo on to the
14th of april, which was called the 18th before the calends of may: the 13th
of april was called idus, the ides of that month; the 12th was pridie idus,
the day before the ides; the 11th, the 3d before the ides; the roth, the 4th
before the ides; and fo on to the 6th day, which was the 8th before the
ides: the 5th day was called nona, being the 9th before the ides; the 4th day
was called pridie nonas, the day before the nones; the 3d day of april was the
3d before the nones; and the 24 day, the 4th before the nones: all theſe reck-
onings were inclufive, and took in the days of the calends, ides, and nones.
The ides of march, may, july and october were the 15th days of thoſe months;
in the other months the ides were the 13th days.
a By Solon who reformed the Grecian months to the motion of the moon.
b Odyf. ξ ν. 162. Το μεν φθίνοντος μήνος τε δ' ισαμενοιο
Ισαμενοιο ενετωίος η αρχομενο Hefychius.
c In theſe expreffions pridie calendas, tertio nonas, quarto idus, &c. ante is underſtood, as pridie ante calen-
das, tertio die ante nonas, quarto die ante idus. ante diem, i. e. ante diem confectum hoc eft in ipfo die, Petav.
de doctrina temporum vol. i pag. 236.
1249
CHAP. 13.
519
ASTRONOMY
1249 The ancient Roman week, as it may be called, confifted of 8 days,
the ninth was a kind of market day for the country people to come to town and
tranſact ſuch buſineſs as they had there. In an old Roman calendara cut upon
marble, and ſuppoſed by Grævius to be done in the time of Augufius Cæfar,
every 8 days have prefixed to them the firft 8 letters of the alphabet, ABCD
EFGH: in imitation of this, the 7 days of the Chriſtian week are marked
in our calendars with the first 7 letters; whereof one that points out the dies
dominica the Lords day or funday is called the dominical or funday letter.
1250 The firſt day of january is every year marked with the letter A, the
other letters BCDEFG follow in order through every month in a common
year of 365 days: theſe make 52 whole weeks and one day, and therefore
if we confider any two common years immediately following one the other,
the laſt of december in the first year muſt have the letter A fet againſt it, and
the ſecond muſt begin with the fame letter; ſo that A comes twice together
and muſt denote different days of the week in the two different years, and
change the dominical letter to that immediately preceding; therefore, if B
were the dominical letter in the firſt of theſe years, it would be A in the ſecond:
this change would go through all the feven letters in feven common Julian
years; but, as every fourth year is biffextile or leap year, confifting of 366
days, the intercalation of a day in february cauſes the dominical letter in that
year to be changed twice; once immediately after the intercalation, and again
at the end of the year: and theſe changes are not all gone through in leſs than
4 times 7, or 28 years; this period of time comprehending all the variations of
the funday letter in the old calendar, is commonly called the cycle of the fun.
1251 The obſervation of the feaſt of Eafter is of great antiquity, as ap-
pears by the diſputes about the day whereon it was to be kept, which dif-
turbed the peace of the Chriftian Church before the first council of Nice.
That our bleffed Saviour was crucified on a friday and roſe from the dead on
the funday following appears from the hiftory of the Evangelifts; and upon
this account the one day in feven, ordained to be kept holy in memory of the
creation of the world finiſhed in fix days, was changed from the feventh day
of the week whereon God is faid to have refted or ceafed from his work, to
the first, the day whereon our Lord by his refurrection from the grave fhew-
ed that he had compleated the great work of the redemption of mankind.
This change of the fabbath day is juſtly ſuppoſed to have been made by apof-
tolical authority: and accordingly we find the firſt day of the week called
the Lords day by St. John b. The primitive Chriftians were defirous of keep-
ing Eafter, the memorial of our Lords refurrection, as near as poffible to the
a Scalig. de. emendat. temp. p. 232. Græv. Thefau. Rom. antiqu. tom. 8.
3 U 2
b Rev. c. 1. V. 10.
time
520
BOOK 3.
ASTRONOMY
time of the year wherein that glorious victory over death was obtained: for
this purpoſe they could have no better guide than the Jewiſh paffover.
1252 The Jews were by divine appointment ordered to keep the paffover
on the 14th day of the month abiba, called afterwards nifan. This month.
was to be the first month of their year, Exod. c. 12 v. 2.
The Jewiſh year
and month being lunar, they did not call that the new moon, or firſt day of
the month, when the mocn was in conjunction with the fun, but the day
wherein after conjunction the new moon first appeared in the evening. It has
before been mentioned that the Jews began the day at funfet, § 1211. In
Judea the air is fo clear that the new moon is often ſeen within leſs than
24
hours after conjunction.
They were particularly careful in fettling the first day of nifan on ac-
count of the paffover to be kept on the 14th thereof; while the temple ſtood,
and for many years after, this was done in the following manner; at the lat-
ter end of the year the Sanhedrin or great council at Jerufalem, who had the
fole direction of this affair, met to confider when the next new moon was
to be expected; this might either be known by ſuch tables as they had or by
reckoning from the laſt new moon; and on the laft day of the year they fent
feveral perfons not fewer than two of good character and credit to ſome emi-
nence, ordering them to watch for the firſt appearance of the new moon af-
ter funfet, and, as foon as they had a view of her, to return and give them
an account thereof: when this was done, after a ſtrict examination of the
perfons fent, the next morning the head of the council declared the new moon
to be come, in this form of words, it is confecrated; it was then publiſhed
at Jerufalem, and notice thereof given to the country round, for ſome time,
by lighting up beacons placed before for that purpofe; but, afterwards, up-
on finding that ſome of their enemies fet up falfe lights to deceive the peo-
ple,
they left off the beacons, and fent meffengers round about as far as a
ten days journey would reach: as for thoſe who lived too far off to receive
the decifion of the council in time, they kept two days holy, the thirtieth
and thirty firſt from the laſt new moon, that they might be ſure to keep the
feaſt of the new moon on the fame day with their brethren in Jerufalem.
When by reaſon of cloudy weather the new moon could not be feen in
her proper time, that is on the beginning of the thirtieth day from the laſt
new moon, the council declared the thirty first to be the new moon, becauſe
the lunar month cannot reach farther than thirty days, fo that the month
adar confifted that year of thirty days; fometimes when the new moon
a Abib fignifies an ear of corn with the ſtalk, fome tranſlate it the month of new corn, i. e. when coin is
firſt ripe, which in Egypt and Judea was about the vernal equinox, v. Schindler in
could
CHAP. 13.
521
ASTRONOMY
could not be ſeen by thoſe who were employed by the council, other per-
fons from other places would come and declare they had ſeen the moon in
her proper time: theſe voluntary meffengers were very ſtrictly examined and
crofs queſtioned, but if they were of unblemiſhed reputation and gave their
evidence ſteadily and upon oath, the council would ſometimes pay fo much
regard to their teftimony as to recall the declaration they had made of the
new moon which they had fixed for the thirty firſt day, and publiſh it for the
thirtieth: and, if they did not make any change in the day upon their infor-
mation, they uſed to entertain and reward them; that others might be en-
couraged to look for the new moon, and to take a journey to inform them
thereof a.
1253 But, befides this change of a day in fettling the firſt of nifan, there
was upon
fome occaſions an intercalation of a whole month of 29 or 30 days
made ufe of; as when the corn was not ripe enough, when lambs and kids
were not forward enough, when, by reaſon of floods and breaking down of
bridges, the roads to Jerufalem were impracticable, when their ovens in which
the pafchal lamb was to be roafted or broiled were demoliſhed, with fome
other reafons whereof the council were the fole judges. I have mentioned
all this to fhew that there is no finding out the year of our Bleffed Saviours
crucifixion by any aftronomical calculation, becauſe it is uncertain in what
manner the Jews that year fixed the firſt of nifan; whether on the thirtieth
or thirty firſt day from the firſt of adar: and it is alike uncertain whether
they intercalated a whole month that year or not. Or if they did whether the
month intercalated were of 29 or 30 days.
If the Jews had made ufe of the Julian year, and always kept their paffover
on the 14th of march, or if they had always kept it on the day of the aftro-
nomical full moon upon or next after the vernal equinox, as we can afcertain
the time of our lords crucifixion within 4 or 5 years of the truth, we ſhould
then only have wanted to find out in which of thoſe 4 or 5 years the 14th of
march or the before mentioned full moon was on a friday, and that would
have characterized the very year; but this was not the cafe: the Jewiſh year
in our Saviours time was irregular, as the beginning of it depended not up-
on the conjunction of the fun and moon, but upon the first appearance of
the moon after conjunction, as fettled by the Sanhedrin ©.
a Mishnah. c. de principio anni, et ibi Maimonid. et Barterona. v. etiam Maimon. de confecratione calend.
et de intercalatione.
b It ſeems they roaſted the paſchal lamb in a place fomething like one of our ovens,
for if any part of the lamb touched the fhell over it, that part muſt be cut off and caſt away, as being roaſted
by the ſhell and not by the fire. Cateros in torrendo pafchali agno ritus quere apud Maimonid. de facrificio paf
chali. c de Judæorum anno Chrifti facalo, v. Petav. de doctrina temporum, lib. 2. cap. 27.
1254
522
воок 3.
ASTRONOMY
1254 Befides the octennial period or cycle mentioned § 1239, the Jews
are faid to have made ufe of one of fourteen and another of eighty four years:
whatever cycles they were directed by, they are thought to have been in our
Saviours time fo erroneous in keeping their paffover as to have been two or
three days out in their reckoninga: if this be true it muſt be owing to the
fettling wrong the firſt of nifan, becauſe they always killed the paffover on
the fourteenth of that month.
1255
The fourteenth of nifan being the Jewish paffover, whatever day of
the week it fell upon, was obferved as the Chriftian feaſt of Eaſter for fome
time by the eaſtern Churches, whereof many members were converts from
Judaiſm, whereas in moſt of the weſtern Churches the feaſt of the reſur-
rection was kept always on a funday: to bring them to an uniformity was
one of the reaſons for which the council of Nice was called together by Con-
ftantineb: it was then determined that it ſhould be on the funday after the
firſt full moon upon or next after the vernal equinox, which equinox at that
time in common years was on the 21t of march. This determination is not
among the canons of the council, but may be ſeen in their fynodical epiſtle
preferved to us by two ecclefiaftical hiftorians, Socrates and Theodoret.
1256 The Metonic cycle of 19 years mentioned before, § 1241, was at that
time thought exact enough to point out the new moons, in Julian years then
in uſe, in order to find the paſchal limit or the full moon that was to direct the
keeping of Eaſter; for this purpoſe calendars were publiſhed wherein golden
numbers as they were called, were ſet againſt ſuch days as would have new
moons in every year of the cycle, as will be explained § 1261: this would
anſwer the purpoſe for a confiderable time, not varying from the truth more
than an hour and an half in 19 years, ſo much do the new moon return to
the fame fituations before the completion of nineteen Julian years, which
amounts to about 8 hours in a century: this error they might perhaps think
not confiderable enough to deſerve their notice, or might leave it to be cor-
rected by pofterity, when it arofe to a whole day, as it does in about three
centuries; ſo that in the number of years elapfed from the council of Nice to
the year 1582, when the calendar was corrected by Pope Gregory, the moons
motion had anticipated fo much that the golden numbers pointed out the
new moons above four days too late; and in 1752 when the Britiſh calendar
was corrected, they gave them almoſt five days too late.
a For this reaſon we cannot hope to diſcover the exact time of our Lords crucifixion by aſtronomical cal-
culation, but muſt have recourſe to ecclefiaflical hiſtory. v. Petavii animadvers. in Epiphanium de hærefi
Alogorum et de doctrina temporum, lib. 12.
b v. Ejus epiftolam apud Eufeb. de vita Conftantini.
v etiam Jofephum Egyptium apud Bevereg. Pandect. canon. vol. 1. p. 685.
1257
CHAP. 13.
523
ASTRONOMY
1257 The golden number ſo called from its ufe, or from being fet down
in letters of gold, called alfo the prime, proceeds from 1 to 19, and ſhews
the year of the cycle of the moon: thus, the firſt year of the cycle the gol-
den number is 1, the fecond year 2, the third 3, &c. This cycle is gone
through in 19 years, after which it begins again and goes on as before.
1258 The golden numbers had generally annexed to them a table of epacts:
the epact fet againſt any year fhewed the age of the moon on the firft of march
that year, or the number of days then paffed fince her laft conjunction with
the fun; from whence it was eafy to find the age of the moon for any day
of the month in that year, which was the principal uſe of epacts before the
correction of the calendar.
1259 The table of epacts was made by the following method: the lunar
year being 354 days, II days fhorter than the folar, (in this affair only whole
days are confidered) eleven was taken for the epact of the first year; and the
fame number II added to the epact of the year immediately preceding, cafting
away 30 as often as by addition that fum arifes, fhews the epact of every year of
the cycle: thus, fuppoſe on the firſt day of march in a given year, the moon to
be in conjunction with the fun; in the year immediately following the moon
will have run through 12 lunations and be again in conjunction 11 days be-
fore the fun has gone through his annual courſe and brought again the firſt
of march; and confequently the moon will on that day be 11 days old: at
the end of another year the age of the moon will be 11 days more, that is
22 days: in the third year 11 days added to 22 the epact of the fecond year
make 33, from which number 30 muſt be caft away, becauſe 30 days make
a whole month, and the epact for that year is 3: for in three ſolar years the
moon will have gone through 37 lunations, or three lunar years one month
and three days; that is ſhe will after having been in conjunction 37
times be 3
days old on the first of march, at the end of the third year: thus the table of
epacts is made by adding 11 every year to the epact of the foregoing year, and
caſting away 30 as often as by fuch addition the fum arifes to that number of
days. The table reaches to 19 years only; becauſe when that number of years is
gone through, the epact begins again at II, and goes on in the fame manner
another 19 years, and fo on for ever, as was ſuppoſed.
The beginning of the first cycle of the moon juft now mentioned was on
the first of january in the year before our Saviours nativity, according to the
Dionyflan or vulgar account: therefore the golden number is found at any
time by adding one to the year of our Lord then current and dividing it by
19: thus, in the year 1760, divide 1761 by 19 the quotient is 92, fo ma-
ny entire cycles have elapfed fince that time, and the remainder 3 is the gol-
4
den
524
BOOK 3
ASTRONOMY
is
den number for the year 1760: if there be no remainder the golden number
19.
The golden number being given the epact before the correction of the
calendar was known by the following table.
Golden
Number. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10|11|12| 13 |14|15| 16 | 17 | 18 | 19
Epa&t. |X1|XXII|III|XIV|XXV|VI|XVII|XXVIII|IX|XX|I |XII|XXIII|IIII|XV|XXVI|VII|XVIII|XXIX
By this table it appears that the golden number was an index to the epacts,
golden number 1, epact XI, golden number 2, epact XXII, &c.
1260 It is generally thought that the golden number and epacts were in-
vented by the Chriſtians of Alexandria, or that they were the firſt who ap-
plied them to find the pafchal limits ª: that city had fo long been a famous
fchool for aftronomy, that in the early ages of Chriſtianity the Biſhops of
Alexandria were often confulted about the proper time of keeping Eafter.
The Egyptians, who as was faid § 1235, had formerly a wandering year,
after the victory of Auguſtus over Antony and Cleopatra, fettled it in the Julian
form, but with a different beginning; for the first day of their firſt month
called thoth anſwered to the twenty ninth of auguft in the Roman year.
1261 Both the golden numbers and epacts are faid to have been placed in
the Alexandrian calendar, to point out the new moons: the Romans copied
it, but with fome variation; for they retained january for the firſt month,'
and omitting the epacts, fet down only the golden numbers againſt ſuch
days as would have new moons: theſe numbers appear to proceed irregular-
ly, and fometimes by leaps; there being fome days which have no golden
number affigned to them; becauſe thoſe days can never have a new moon
happen upon them for a great number of years. The method of placing the
golden numbers as they ſtood in the calendars before the Gregorian correction
was as followeth, they calculated on what days of the ſeveral months the
new moons would happen in the firft, fecond, third, and every other year
of the decennoval cycle, and againſt each day whereon there would be a
new moon in the first year of the cycle they placed the number I: againſt
each day whereon a new moon would fall in the fecond year they placed
the number II: and fo on through the whole calendar: fo that the golden
numbers pointed out every new moon through the nineteen years. Thus in
the ſpecimen here given of part of the month of january, the number III is
put againſt the first day to fhew that in the third year of the cycle, when the
golden number is III, there would be a new moon on the firſt of january: the
fame fpecimen fhews there would be a new moon on the third of the fame
a Petav, doctr. temp. 1. 6. c. 1. Bela de temporum ratione c. 42. de cycla decennovali.
month,
CHAP. 13.
525
ASTRONOMY
month, in the years when the golden number is XI; as alfo a new moon on
the fifth, when the golden number is XIX: on the fixth, when the golden
number is VIII, &c.
golden number
January
III
XI
XIX
VIII
XVI
I
2
4
5
~ 3+ no N∞
760
&c. &c.
days
This difpofition of the golden numbers is the
fame as is found in Bede who flouriſhed in the
ſeventh century, in the calendars of the Roman
Breviaries, from that time to the time of the Gre-
gorian correction, and in our common-prayer
books before the year 1752; the defect thereof
has been already mentioned § 1256.
1262 The decennoval cycle has before been faid to bring the new moon
to the fame day of the month, by means of feven emboliſmic months as they
were called: in which of the nineteen years thoſe additional months were
inferted by the ancient Greeks has been mentioned in § 1241: the Chriftians
made fome change in the fituation of them; according to Bede, they inferted
them in the third year, in the fixth, the eighth, the eleventh, the four-
teenth, the feventeenth, and the nineteenth.
The firſt fix emboliſmic months were each of thirty days; that in the nine-
teenth year contained only twenty nine days: this was in order to bring it
about that the first year of the cycle immediately following might have ele-
ven for its epact; and that all cycles of the moon, having the fame begin-
ning might be fimilar, and proceed in the fame manner:
for the epacts before the correction of the calendar.
fo much
1263 In fettling the Gregorian calendar they made ufe of a table of gol-
den numbers and epacts; but in the calendar itſelf the golden numbers were
omitted and twenty nine epacts or as the author calls them epactal numbers
inferted, which with an addition of the mark * made the number thirty;
and theſe were placed one of them againſt every day of each month through-
out the year, in the following manner: againſt the firſt of january ſtood the
mark*, againſt the fecond the number XXIX, againſt the third XXVIII,
and ſo on, diminiſhing an unit every day, which brings the number I to be
fet againſt the thirtieth of that month, and * to the thirty first: continuing
the feries in this manner, XXIX anſwers to the first of february, XXVIII
to the fecond, and fo on through all the months to the 20th of december,
where, the ſeries of epacts having been repeated 12 times, against the 21st of
3 X
that
526
BOOK 3
ASTRONOMY
that month was fet the mark *, againſt the 22d the epact XXIX, againſt
the 23d the epact XXVIII, &c. So that the laſt 11 days of december had
the fame epactal marks as the first 11 days of january.
a ſpecimen of part of the months of january and february.
Here followeth
January
February
cycle of epacts.
dominical letter. days.
cycle of epacs.
*
A
XXIX
XXVIII
XXVII
b
1 2
I
C
3
d
XXVI
e
25. XXV
f
XXIV
go
7
XXIII
A
450 noo
8
XXIX
XXVIII
XXVII
25. XXVI
XXV. XXIV
XXIII
XXII
XXI
&c.
&c.
&c.
f
g
4
A
b
C
d
123+ no noo
&c.
&c.
&c.
dominical letter. | days.
d
e
I
As there are but 19 years in the cycle of the moon, there can be but 19
epacts in uſe in the fame age; but in procefs of time they vary fo that
all the thirty will come into uſe in their turns: but the fame ſeries of epacts
does not return in leſs than about 7000 years.
1264 Befides the epactal numbers expreffed by Roman letters, every month
has 25
25 in the common figures fet againſt one of theſe numbers xxv or XXVI;
and that alternately: and a rule is given to this effect, that the epact xxv in
Roman letters is to be in ufe when the golden number it belongs to is leſs
than 12; but that 25 is to be taken for the epact when the golden number
is 12 or more: thus, in the fecond table § 1266, under the golden number 6
we find the epact xxv, but in the third table we have 25 under the golden
number 17. In fix places of the calendar two epacts namely xxv and xxiv
are fet to the fame day, in order to bring the lunations to be alternately of
29 and 30 days; for if the 30 epacts were to proceed through the
year in
the fame manner as they do in the firſt ſeries of them in january, 12 times
30 would make 360, which exceeds the number of days in the lunar
by 6; to prevent this, fix of the months, namely, february, april, june, au-
guft, feptember and november, have each two numbers xxIV and xxv to
one day, whereby the epactal numbers are reduced to ſtand againſt only 354
days the number of days in the lunar year, fo as to leave the laſt 11 days of
december to begin with * xxx, xxXVIII, &c.
year
I
The
CHAP. 13.
527
ASTRONOMY
The uſe of epacts is to point out the new moons by the following method:
find the golden number of the given year by § 1259, that being known the
epact is found by the table or ſeries of epacts then in uſe, an example will
make all eafy; I would know the new moons for 1760: the golden number
for that year is 3 by § 1259, the epact is xxII, as appears by the ſecond table
given § 1266, which is in uſe in the preſent age, and will laſt till 1900:
every day then in the calendar to which the number xxII is fet will be a
new moon in the year 1760. It was neceffary to refer to the table then in
uſe, becauſe different ages require different tables § 1266, 1267.
The uſe of 25 for an epact is this, in fome ages the numbers xxv and xxiv
may be both in ufe as they are in the third table; in which caſe they would
indicate the new moon to fall upon the fame day of the month twice in 19
years, contrary to aſtronomy: to prevent which, 25 is then given in the table
inſtead of xxv, and in thofe months wherein xxv and XXIV are fet to the
fame day 25 is fet to XXVI, one day nearer to the beginning of the month.
1265 The moon anticipates, that is, new moons come earlier than the cycle
of 19 Julian years points them out by one day in 312 years and an half, ac-
cording to the tables made uſe of by the compilers of this calendar; how-
ever, they thought proper to make their corrections at the ends of whole
centuries, as being more remarkable and lefs liable to be forgotten than odd
numbers of years; accordingly, they put the new moon forward one day at
the end of each 300 years 7 times fucceffively, which amount to 2100 years:
and in order to account for the odd 12 years and an half, they deferred
putting the moon forward for the 8th time to the end of 400 years, when
the period of 2500 years is compleated: thus one day is to be taken out of
the lunar year, that is it muſt be made one day fhorter, in the years 1800,
2100, 2400, 2700, 3000, 3300, 3600, 3900, 4300, &c.
1266 As ten days had been fuppreffed in the calendar, and the moons mo-
tion had anticipated four days fince the council of Nice, as was mentioned
§ 1256, it became neceffary, to make a proportional change in adjuſting the
table of epacts to the golden numbers; for this purpoſe, they made new cal-
culations of the times of the new moons, taking the length of the year from
the Alphonfine tables, and the length of the fynodical month from Tycho
Brabe: and gave three tables of golden numbers and their correfponding
epacts: the firſt table was calculated to ferve from the year of correction
1582 to 1700: the fecond was to be made ufe of from 1700, when the
firſt rule in § 1267 takes place, to 1900; for by the third rule no change is
made in the year 1800: the third table would be good from the year 1900,
3 X 2
when
528
BOOK 3.
ASTRONOMY
when the firſt rule again takes place, to 2200; for by the third rule no change
is made either in 2000 or 2100. The tables here follow.
A TABLE OF EPACTS ANSWERING TO THE GOLDEN NUMBERS FROM THE
YEAR OF CORRECTION OF THE CALENDAR 1582 TO 1700.
G. Numb. 6 | 7 | 8 | 9 |10|11|12|13| 14 |15|
13 | 14 | 15 | 16 | 17 | 18 | 19 | 1 | 2 | 3 | 4 | 5
Epacts. xxvi vii | xviii | xxix | x | xxi | ii | xiii | xxiv | v | xvi | xxvii | viii | xix | i | xii | xxiii | iv | xv
A TABLE OF GOLDEN NUMBERS AND THEIR EPACTS FROM 1700 TO 1900.
G. Numb. 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Epacts. ixxx | i | xii | xxiii | iv | XV | xxvi | vii | xviii | * | xi | xxii | iii | xiv | xxv | vi | xvii | xxviii
|
A TABLE OF GOLDEN NUMBERS AND EPACTS FROM 1900 TO 2200.
G. Numb. | 1 | 2 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |12| 13 | 14 | 15 | 16 | 17 | 18 | 19
Epacts. xxixx xxi | ii | xiii | xxiv | v | xvi | xxvii viii | xix | * | XII xxii iii xiv | 25 | vi | xvii
I
1267 As the Gregorian calendar was defigned to be perpetual, fome rules
were given whereby tables might be made of golden numbers and epacts
that ſhould ferve for future ages, in like manner as the three tables. now gi-
ven were to be in ufe from 1582 to 2200: fome of thofe rules are prefixed to
the calendar of 1582 publiſhed by Lilius in that year, wherein he refers to
a larger account of his method, which I cannot find was ever printed, per-
haps he was prevented by death: Clavius who had been one of the committee
that met at Rome about the calendar, and were ten years in fettling it, fup-
plied that defect in a large work wherein he reprinted the treatiſe menti-
oned § 1244, and the firft calendar publiſhed by Lilius, explained the me-
thod of conſtructing the fame, and defended it againſt the attacks of Mæflinus
Vieta and Scaliger: from him the three following rules are taken which ſhew
how the epacts are to be corrected from time to time in order to keep them
right, notwithſtanding the change of the times of new moons arifing from
the moons anticipation before mentioned. Clavii, oper. tom. 5.
Rule 1. When the hundreth year or the last year of a century is a com-
mon one, the biffextile being omitted, § 1245, and the moon wants no cor-
rection, the epact then muſt be diminiſhed an unit; becauſe the folar year
is then ſhortened one day, and the lunar continues the fame: thus in the fe-
cond
CHAP. 13.
529
ASTRONOMY
cond table the epact to the golden number 8 is xvii, an unit leſs than in the
firſt table where the epact to the fame golden number is xviii.
Rule 2. When the hundreth year is biffextile and the moon wants cor-
rection, every-epact is increaſed an unit: becauſe the folar year is then the
fame, and the lunar is fhortened one day.
Rule 3. In the hundreth year when the biffextile is omitted and the moon
corrected, or when the biffextile is not omitted and the moon wants no cor-
rection, no change is made in the epacts: becauſe in the firſt cafe both folar
and lunar years are ſhortened a day, in the fecond cafe both continue the
fame without alteration.
1268 Clavius has given 30 feries cf epacts which take in all the variety of
them that can happen; he has alfo given tables with directions to find by them
which ſeries of the 30 will be in ufe in any of the feveral ages of the world
as far as the year of our Lord 303300, if the world ſhould laſt ſo long. None
of theſe ſeries will be in ufe for leſs than 100 years at one time, fome will
laft 200, and many of them 300 years.
1269. In the correction of the British calendar we have followed the Gre-
gorian in all points, except that we have made uſe of the golden numbers
only, omitting the epacts; and have placed the golden numbers not againſt
the days which will have new moons, but againſt the days of full moons ;
and only againſt the full moons of the paſchal months march and april, in
order to find out the time of Eafter: in the rest of the months they are omit-
ted, as being of no other uſe than to find the age of the moon, which is
better known by our common almanacks that are in every bodies hands.
In the Britiſh calendar alſo are given tables for changing the places of the
golden numbers, when the omiffion of the biffextile or the anticipation of the
moon requires it; but we have not extended our view fo far as Clavius has
done: we have provided for keeping the calendar right to the year of our
Lord 8500; which is far enough for us to look forward.
Scholium. It is indifferent whether new moons are fhewn by fetting againſt
the days of them golden numbers or their correfponding epacts: the compilers
of the Gregorian calendar ufed epacts for that purpoſe, becauſe they could
be contrived to ſtand therein without any alteration. In correcting the Britiſh
calendar the places of the golden numbers were found from the places of
their correfponding epacts, and each golden number was fet not againſt the
day of the new moon but againſt the 14th day after, which would be the
full moon according to the ecclefiaftical account, wherein the intention was
not to attend ſtrictly to the true motions of the fun and moon, but to find a
cycle that ſhould be eaſily underſtood, and that ſhould ſecure the three prin-
cipal
530
BOOK 3
ASTRONOMY
cipal points fettled by the first council of Nice, 1. that Eaſter might be al-
ways on a funday, 2. after the equinox, 3. after the firſt full moon that falls
out upon or after the vernal equinox: though we have now more correct
tables of the fun and moon than were made ufe of by the compilers of the
Gregorian calendar we follow the fame rules with them.
1270 As the feaft of Eafter is to be celebrated on a funday, in every cycle
that is to determine the time thereof, regard muſt be had to the Dominical
or funday letter, which in the old calendar was found by a cycle of 28 years
called the cycle of the fun, § 1250.
Here followeth a table of the cycle of the fun with the funday letter,
to which is added the cycle of the moon, as they were in uſe in the old ca-
lendar: I take them from 1672, becauſe in that year thofe two cycles began
both together, which happens only once every 532 years.
Ann. Dom.
1672
73
Cycle of | Sunday | Cycle of
the fun. letter.
1 2
GF
E
the moon.
I
1 2
Cycle of
the moon.
Ann. Dom.
Cycle of Sunday,
the fun. letter.
1688
17
AG
17
89
18
F
18
74
3
D
3
90
19
E
19
75 4
÷ 5O NOO
C
4
91
20
D
I
7
8
76
77
78
79
1680
DC
9
BA
G
F
597
92
2I
CB
6
93
22
A
2 3
E
70
94
23
G
4
95
24
F
5
9
96
81
82
IO
B
ΙΟ
97
I I
A
I I
98
27
83
12
Ꮐ
I2
99
28
56 No
2 2
25
26
ED
6
C
7
B
A
al
84 13 FE
13
1700
85 14
D
14
I
86
15
C
15
2
87
16
B 16
•3
I am t
GF
ΙΟ
2
E
I I
3 D
12
4
C
13
4
5
BA
14
1271 In the old calendar the first year of the cycle of the fun was a bif-
fextile or leap year, and had therefore two funday letters G and F; the firſt
of theſe G was the funday letter from the firſt of january to the twenty fourth
of february the intercalary day; F was the funday letter for the remaining
part
+
CHAP. 13.
531
ASTRONOMY
part of the year: in like manner every fourth year being biffextile had
two funday letters, the firſt was in uſe from the firſt of january to the twen-
ty fourth of february; the fecond for the remaining part of the year: the reſt
were common years and had but one funday letter. In the old ſtyle the
cycle of the fun with the funday letter proceeded uniformly in this man-
ner for ever, every 28 years being the fame as the 28 years immediately
preceeding.
To find the cycle of the fun for any given year, add 9 to the year in quef-
tion, and divide the fum arifing there from by 28, (the quotient need not be
regarded for that only fhews how many cycles have elapſed ſince the begin-
ning of the Chriſtian æra) the remainder is the number of the cycle of the
fun required; if there be no remainder 28 is the number: thus, for the year
1760, add 9 to 1760, the fum is 1769, divide this by 28, the remainder 5 is
the cycle of the fun for that year.
This rule for finding the cycle of the fun is of ufe in the new calendar
alfo, but the foregoing table will not now fhew the funday letter; as will
preſently appear.
1272 In the year of correction 1 582 the cycle of the fun was 23, the ſunday
letter G; in fuppreffing ten days there was no alteration made in the days
of the week, but the funday letter was changed; for funday the 7th of octo-
ber marked with G was by the correction made the 17th marked with C: by
this means there began a new progreffion of the funday letters, ſo that the
fame letters would no longer correſpond to the fame years of the cycle of
the fun.
In the Gregorian calendar in every four fubfequent centuries three biffextiles
are made common years, by omitting the intercalations: in this calendar alfo
a common year hath but one funday letter, a biffextile hath two, which take
the fame places in the year as in the old calendar; the cycle of the fun and
the funday letters proceed from 28 years to 28 fubfequent, in the fame man-
ner as in the old ſtyle, to the laſt year of a century, which is changed from
a biffextile to a common year; and this is done in the first three centuries
of every 400 years: theſe three omiffions of intercalary days in every 400
years cauſe each a change in the funday letters, fo that the ſeries of them
does not come exactly into the fame order in leſs than 400 years, as appears
by the following cycle.
A CYCLE
532
ASTRONOMY
BOOK 3
A CYCLE OF THE SUNDAY LETTERS FOR FOUR HUNDRED
YEARS, TO BE REPEATED PERPETUALLY.
1600
1700
1800
1900
Intermediate years
BA
C
E
G
1 2
I 29 57 85
G
B
D
F
30 58
86
F
A
C
E
3
4
| www
59
87
60
88
2∞
E
G
B
D
DC
FE
AG
C B
56 700
33
61
89
B
D
F
A
34 62 90
A
C
E
G
35
63
91
G
B
D
F
solo
36
64
92
FE
A G
CB
ED
37
65
93.
D
F
A
C
ΙΟ
38
66
94
C
E
G
B
I I
12
39
67
95
B
D
F
A
40 68
96
AG
*СВ
ED
GF
13
4I
69
97
F
A
C
E
14 42
70 98
E
G
B
D
15
43
71
99
D
F
A
C
16
44 72
CB
ED
G F
BA
17 45 73
A
C
E
G
18 46
74
G
B
D
F
19
47
75
F
A
C
E
20
48
76
ED
G F
BA
DC
2 I
49 77
C
E
G
B
22
50
78
B
D
F
A
23 51 79
A
C
E
G
24
52 80
GF
BA
DC
FE
25 53
81
E
G
to
D
26
54
82
D
F
A
C
27 55
83
C
E
G
B
28 56
84
BA
DC
FE
A G
In this cycle the funday letters for the hundredth years are thoſe next un-
der each of them, as for 1600 B A, for 1700 C, for 1800 E, for 1900 G.
To
CHAP. 13.
533
ASTRONOMY
To find the funday letter for any intermediate year as 1765, carry your eye
in a ftrait-line towards the right hand from the intermediate number 65 to the
column under 1700, and you have the funday letter for that year F. It is
obvious that by the fame rule the intermediate numbers 9, 37, 93 upon the
fame line with 65 fhew F to be the ſunday letter for the years 1709, 1737,
and 1793.
1273 The following table taken from the calendar publiſhed by Lilius in
1583, fhews how Eaſter is found from the epact and ſunday letter given.
Epacts
Sunday Days of the
letters month
Sunday Days of the
Epacts
Sunday Days of the
letters
month
Epacts
letters
month
xxiii
xi
A
April 2
xxix
F
April 14
xxii D- March 22
X
B
3
xxviii
G
15
xxi
E
23
ix
C
4
xxvii
A
16
XX
F
24
viii
xix Ꮐ
xviii
A
xvii B
xvi
C
~ ~ ~ ~
25
vii
26
vi
27
V
28
iv
DEFCA
5
25. xxvi
B
17
6 xxv. xxiv
C
18
7
D
19
G
E
20
9
F
2I
XV
D
29
iii B
IO
G
22
xiv
E
30
ii
xiii
F
31
xii G April
*
CAE
II
A
23
D
12
B
24
13
C
25
In this table the epacts are fet againſt the days whereon the paſchal full
moons happen in thoſe years whereof they are the reſpective epacts: the uſe
of it here followeth, in the column of epacts find the epact of the year in
queſtion, againſt which towards the right hand ſtands the day of the pafchal
full moon that year, then in the column of funday letters find the letter of
the
year that ſtands next after the day of the full moon, and the day of
the month on the fame line with that funday letter is Eafter day: for exam-
ple, let xx be the epact of a given year, whofe funday letter is A, as it was
in the year 1758, the day of the month on the fame line with the epact xx
is the 24 of march; then carry your eye down the column of funday letters
to the fubfequent A, the day of the month now on the fame line with A
march the 26 is Eaſter day.
In the Britiſh calendar as now corrected there are tables fimilar to this, that
will be in uſe from the prefent time to the year 2199, with this difference
3 Y
only
534
BOOK 3
ASTRONOMY
only that the golden numbers are therein put inſtead of their correfponding
epacts.
1274 If the cycle of the fun 28 be multiplied by 19 the cycle of the moon,
the product 532 is commonly called the Victorian or Dionyfian period: in this
number of years thofe two cycles beginning both at I run each through
ſeveral courſes and begin together again at 1: this is alfo called by fome the
great pafchal cycle, and feems to be originally intended chiefly for finding
Eaſter, for it was ſuppoſed that in 532 years the new moons would return
to the fame days of the month and the fame days of the week; and confe-
quently that Eafter was to be kept on the fame day of the month as in
the fame year of the preceeding period: the beginning of this cycle was by
Victorius the inventor of it fixed at the baptifm of our bleffed Saviour, but
by Dionyfius removed to his nativity. This period will alſo ſerve to aſcertain
the time of paſt tranfactions, for if it be faid of any event that it fell out.
in ſuch a year of fuch a period, or that at the time thereof the cycle of the
fun was ſuch a number and the cycle of the moon fuch a number, the year
is fo characteriſed that no other year can be miſtaken for the fame; for no
other year except one 532 years before or after it, can have the fame num-
bers in both cycles of the fun and moon. Some writers who have made this
uſe of it began the first period at the creation of the world, according to
the account thereof which they thought moft agreable to truth: thus, at
the end of the chronological table of Maximus publiſhed by Petavius in his
Uranologion, p. 355, we have eleven of theſe periods mentioned, with the
times when each of them ended; the firſt is faid to be ended in the 97 year
of Enos, the ſecond in the 130 of Jared, the third in the 142 of Lamech &c.
The fame method of fixing the times of feveral tranſactions related in the
old teftament is made ufe of by the author of a treatiſe de mirabilibus S. fcrip-
turæ, printed among the works of St. Auſtin, but manifeftly of a much later
date; he ſays, for example, that Noabs flood fell out in the 114 year of
the fifth cycle from the creation of the world, &c. Auguſtini oper. pag. 520.
edit. Froben.
1275 The Roman Emperors at their inaugurations uſed to give largeſſes
to the foldiers and the populace, and every five years after to make them freſh
donations: upon
thefe occafions they were faid dare quinquennalia, decennalia,
vicennalia; according as thefe donations were in the fifth, tenth, or twentieth
year of their reign a. Fifteen years were called an indiction: Conftantine gave
his quinquennalia in A. D. 312, the year of his victory over Maxentius, his
vicennalia 15 years after; hence probably the indiction of 15 years took its
a Scalig de emendat. temp. p. 501.
rife
CHAP. 13!
535
ASTRONOMY
rife, and it became customary after Conftantine, in fetting down the time
of a tranfaction to date it in fuch an indiction, as in the firft, fecond, or
third indiction, &c. by which was meant the firft, fecond, or third year of the
indiction then current. The beginning of the first indiction was in feptember
A. D. 312; the Popes bulls began it on the firft of the january following
this period being carried back to the Chriſtian æra will fhew that the nati-
vity of our Lord was in the fourth indiction, that is in the fourth year of
that period: therefore to find at any time the indiction, add
3 to the year
of our Lord and divide the fum by 15, the remainder, if any, is the indiction;
if there be no remainder 15 is the indiction. The greater number of characters
are applyed to any year with the greater certainty is it pointed out: the years
of the cycle of the fun and moon are good marks of time, eſpecially if they are
both fet down: if the indiction be mentioned it aſcertains the year fo that
no other year can be taken for it but one 15 years before or after.
year of
1276 Jofeph Scaliger by multiplying together the numbers of the cycles
of the fun, moon and indiction, namely 28, 19, 15, or, which is the fame
thing, multiplying 532 by 15, produced the number 7980, which he called
the Julian period; becauſe it confifteth of fo many Julian years: the length of
this period is more than fufficient to take in all the tranſactions that have hap-
pened fince the creation of the world; for the beginning of it is above 700
years before that epoch, according to the account moſt generally received. It
is of great uſe in chronology; for, as we may always know in what
the Julian period the current year is wherein we are confidering any account
of paſt time, if we refer any ancient event to its year in the Julian period,
we aſcertain the time exactly; which cannot ſo well be done by ſaying how
many years it was after the first olympiad, or the deftruction of Troy, or
the building of Rome, or any of the epochs about the times of which there
is a diſagreement among chronologers: in effect, the beſt way of fixing any
other epoch is to refer it to the year thereof in the Julian period: thus, in the
chronology of Helvicus, the firſt year of the firſt olympiad is placed in the
3938 year of the Julian period: the building of Rome in the 3962 year of the
fame, &c. According to the Dionyfian or vulgar account, the birth of our
Bleffed Saviour is placed in the 4713 year of the Julian period; confe-
quently if this 4713 be added to any year of the Chriſtian ara it will give
the
year
of the Julian period: thus, 4713 added to 1700 fhews A. D. 1700
to be the 6413 year of the Julian period.
Petavius is very large in the praiſe of this period, which he would have
taken for an inftance of his candor towards Scaliger whom he had ſpent a
great number of pages in abufing; and yet his candor could not be con-
3 Y 2
tented
536
BOOK 3.
ASTRONOMY
tented to let him have the honour of this invention, but he ſays it was taken
from the Conftantinopolitans; who fometimes indeed applied their cycles of
the fun, moon and indiction to their ara of the creation of the world, but
never made uſe of that ara as a period.
CHAP. 14. EPOCHS: ÆRAES.
1277 When aftronomers confider the motion of any of the heavenly bo-
dies, they pitch upon fome fixt point in the heaven from whence they begin
their reckoning: thus, the regreffion of the équinoctial points may be expreffed
by ſaying how much they go back, in any given time, from the interfection
of the ecliptic by a circle of latitude drawn through the firſt ſtar in aries; v.
660. In chronology, to aſcertain the time of any paſt event, fome diftant re-
markable tranſaction, as the creation of the world, the building of Rome is
taken, the time whereof is confidered as a fixt point, from whence the ac-
count is begun this fixt point is called an epocha or araa.
1278 The epoch now moſt common in Europe among Chriſtian nations
is the year of
year of our Lord: this was firft brought into uſe A. D. 527 by
Dionyfius exiguus, who made the beginning thereof on the 25 of march, the
feaſt of the annunciation of the virgin Mary, at which time the conception
or incarnation of our Lord was fuppofed to commence, and his nativity to
have fallen out 9 months after, on the 25 of the december following. Hence it
is that, till the time of Bede and after, events. were dated from the incarna-
tion of Chriſt, and the 25 of march was made the beginning of the year,
eſpecially in ecclefiaftical affairs; but in later times, as the Julian year came
to be more generally received, the firſt of january was taken for the begin-
ning of the year, and it became cuftomary to exprefs the dates of tranſactions.
by the years from the birth of Chrift. It is eaſy to ſee the difference be-
tween theſe two ways of computing, by the following example; if two events
were ſaid to have happened one of them on the 20 of june in the 100 year
of the incarnation, the other on the 20 of june in the 100 year of the birth of
our Lord, there would be a difference of a whole year between thoſe dates.
The first year of the common Christian ara begins on the firſt day of ja-
nuary that immediately followeth the december in which Chrift was fuppofed
to have been born: this epoch came into uſe ſo many years after that tranf-
action, that it is no wonder it ſhould be found not to be exact: fome make
it one or two, ſome four or five years before the vulgar æra, but among the
a Æra is an old latin word for a number; epocha gr. erox fignifies a ftop: Scaliger, de emendatione
temporum. P. 447. ara is a ſeries of years from the epoch to a diftant time.
various
CHAP. 14.
537
ASTRONOMY
various opinions of chronologers, that ſeems to be most approved which places
the nativity two years earlier than the common account. See Scaliger de
emend. temp. Petavius de doctrina temp. and Strauchius in his breviarium
chronologicum: the laſt mentioned author gives the opinions of fifty writers
on this fubject. See alſo the preface to Prideaux's connection.
In England we had formerly two beginnings of the year, the firſt of janu-
ary
and the 25 of march; fince the correction of the Britiſh calendar by act
of parliament in 1752, we have only one beginning, the firſt of january :
nevertheleſs in ſettling the times of payments of rents, &c. we ſtill retain the
ancient quarter days of the year, namely, the feaſt of the annunciation, of
St. Michael, St. Thomas, and St. John Baptiſt.
7
751
The vulgar Chriftian epoch may be made uſe of as well to aſcertain the
times of paſt events that fell out before as thoſe that happened after it: thus,
Helvicus in his chronological tables places the deſtruction of Troy in the
year before Chrift; and this method gives us a clearer idea of the diſtance
of that event from the preſent time than it does to fay in what year of the
Julian period Troy was deftroyed.
1279 The day of our Lords nativity has alſo been a fubject of
great con-
troverſy, as may be feen in the authors juft now quoted: the 25 of december
was not, according to Scaliger, in the weſtern Churches affigned to com-
memorate that bleffed event, till after Conftantine; nor was it received in the
Greek Churches till the time of Chryfoftom, who fays it was not ten years
fince the obfervation of that day came to their knowledge.
The Church hath with good reaſon appointed anniverſary feſtivals in
memory of the birth and paffion of our bleffed Saviour, and of feveral the
moſt remarkable paffages of his life: whether the times of thoſe folemnities
anſwer exactly to the times of the original tranſactions or not, we need not
be extreamly follicitous, as it is a thing impoffible for us to know with any
certainty, and if known would be of more curiofity than utility; it is of
much greater confequence to be carefull that the commemoration of thofe
events wherein we are fo greatly intereſted be accompanied with proper fen-
timents of holy joy, gratitude, and devotion.
:
1280 To the vulgar Chriftian epoch, we may refer all other epochs;
among which that of the creation of the world ought to be mentioned in the
first place: it is only made ufe of by Jews and Chriftians; the time thereof
is matter of great controverfy.
Among the ancient philofophers there were a few atheiſtical ones who
were abfurd enough to imagin that this beautiful frame of the univerſe was
produced by chance, or a fortuitous jumble of atoms; but far the greateſt
part
538
ASTRONOMY
BOO K3
part
of them held that the world was made, and that it was the work of an
intelligent being. It was a maxim among them that nothing could be pro-
duced out of nothing, and therefore they all agreed in afferting the eternity
of matter, that it never had been generated or made, and confequently
could not be deſtroyed or annihilated a.
Some of them were of opinion that the world muſt have exiſted from eters
nity, and that, as light is from the fun, the world was an emanation from the
fupreme being; whom they conceived to be perpetually exerting his
power, in
framing and ordering his work: fo that, according to this notion, there had
been an infinite fucceffion of worlds formed, diffolved, and reftored, before
the preſent ſtate of things.
Others held that the world was made in time; but at the diſtance of fo
many ages; that it would be a vain attempt to endeavour to find out how
many years had elapfed fince the formation thereof.
Varro the moft learned man among the Romans divided the then paſt
ages of the world into three great periods, the firſt of theſe from the be-
ginning of the world to the flood he called uncertain or unknown; think-
ing it impoffible to diſcover the length thereof, or to know with any certainty
any of the tranfactions that fell out therein: the interval between the flood
and the firſt olympiad he named the fabulous time: from the firſt olympiad
to his own age he called the hiftorical time, as moſt of the facts related to
have been done in that interval were authenticated in written hiftories that
might be looked upon as deferving belief b
1281 There were among the ancient heathens remains of traditions, both of
the creation of the world and the flood; but much diſguiſed by fable: this, and
the want of true hiſtory of very ancient times, gave room for hiftorians to
gratify their own vanity, or that of their Princes and countrymen, by raifing
the beginning of their Kingdoms and States ſo high, as to be many thouſands
of years earlier than the creation of the world, according to the beſt accounts
that we have thereof.
The Egyptians, in order to vouch for the antiquity of their nation, ex-
hibited a ſeries of their Kings fo immenſely large that, if it were not quite
fictitious, has been by learned men thought to have been compofed by plac-
ing in a continued fucceffion as Kings of all Egypt a number of petty Princes,
who were contemporary, and reigned over different provinces .
The Chaldeans are faid to have made like extravagant pretences to anti-
quity 4, which appear as ill founded, by the low date of the moſt ancient
a Cudworth. intelle&t. fyftem, book 1. c. 4. b Cenſorinus, de die natali, c. 21. c Marſham, canon
chron .fecul. 1. d Syncell.chronograph. p. 14, 18, & 35
aftron-
CHAP. 14.
539
ASTRONOMY
a.
aftronomical obſervations that Callifthenes was able to find among them in
the time of Alexander the great, none of which were above 1903 years old ª.
Some Chineſe writers are alſo ſaid to have placed the original of their
nation ſo high as to anticipate many thouſand years the creation of the world,
as we have good reaſon to ſettle it, but their beſt hiſtorians are ſaid to look
upon
all relations before Fo hi as uncertain and fabulous: and though they
name five Kings between him and Yao, who began his reign about 2500 years
before Chrift; they give nothing befides their names; mentioning neither the
length of their reigns nor their actions b. Some learned men have thought
Fo hi to have been another name for Noah, who with ſome of his deſcendants
retired to that part of the world, before the diſperſion of mankind occafioned
by the confufion of languages. See Shuckford's connection, v. I. p. 29 & 102.
1282 What no other writing can do, the moſt ancient of all writings, the
the books of the old teftament will help us to the knowledge of the age of
the world, and the time of the creation thereof; not indeed with accuracy
and certainty as fome pretend, but fufficiently fo, to fatisfy a reaſonable man
in a matter of fuch difficulty. When we fet down the diſtances of the hea-
venly bodies, we do not pretend there may not be an error of ſome thouſands
of miles; and when we fettle the time of the creation of the world we can-
not be fure we do not make it fome hundreds of years earlier or later than
the truth.
1283 Great part of this uncertainty arifes from the difference there is in
our bible, between the Hebrew copies now in being and thofe of a very an-
cient tranſlation thereof in Greek commonly called the feptuagint, in the
ages of the antidiluvians, and of thoſe born after the flood before Abraham:
in the feptuagint the lives of moſt of the perfons are fet down ſo much
longer than in the Hebrew, that, if we compute the time beteen the creation
and the flood by the former, it will come out 606 years more than by the
latter: according to the feptuagint, from the creation to the flood there are
2262 years; according to the Hebrew text, no more than 1656.
There is alſo a like difference in ſetting down the ages of thoſe born after
the flood before the birth of Abraham: the feptuagint afcribes longer lives.
to many
of them than the Hebrew does; and, befides this, between Arphaxad
and Sala takes in a fecond Cainan, not named in the Hebrew, faid to be
130 years, old at the birth of Sala: fo that, upon the whole, the interval be-
tween the flood and the birth of Abraham is 1072 years according to the fep-
tuagint; but according to the Hebrew, only 292: the difference is 780 years.
a. Simplicius in Ariftot. de cœlo, p. 123. ed. Aldin. b Martin. hift. Sinic. 1. 1. Du Halde, p. 264 ed. Par,
The
540
BOOK 3
ASTRONOMY
The time from the creation of the world to the exodus, or going out of the
children of Ifrael from Egypt, is taken from the books of Moſes: the other
intervals, from the exodus to the building of the temple, from the temple to
the captivity of Zedekiah, are all gathered out of the books of the old teſta-
ment: the time from the captivity to the birth of Chrift is made out from
Jofephus and fuch hiftorians as write of thoſe Kings and States who had any
tranfactions with the Jews, compared with each other and with the Evan-
gelifts; but the 19 year of Nebuchadnezzar in which the captivity of Zede-
kiah is recorded to have happened is with great certainty connected with the
common Chriſtian æra by the canon of Ptolemy.
1284 From the creation to the nativity of our Lord, the greateſt part
part of
thoſe who follow the Hebrew account reckon about 4000 years. The Greeks
who uſe the feptuagint compute the interval between the creation of the
world and the beginning of the Chriſtian æra at about 5500 years. I have
given both computations in round numbers, that they may be more eafily
remembered: it is in vain to pretend to exactneſs.
1285 It would be going too far from my ſubject to enter into the diſputes
among
the learned about theſe two accounts, whether the Hebrew or that of
the feptuagint is to be preferred: Strauchius hath treated thereof at large in
the book before cited, as hath alſo the learned Shuckford, in his connection
of the facred and profane hiftory, vol. 1. from page 44 to the end.
1286 It was mentioned § 1280, that the epoch of the creation was made
uſe of by the Jews as well as the Chriſtians; but it muſt be obſerved that the
modern Jews do not make the time of the creation ſo ancient as even the
Chriftians do who follow the Hebrew account, by near 200 years: the
learned are not agreed upon what foundation this epoch ftands; it has been
ſuppoſed that the Jews, in hatred to the Chriſtian name, mutilated their an-
cient chronology, by fhortening fome of the intervals between the building
of the first and the deftruction of the ſecond temple.
1287 An ancient epoch in the heathen world was that of the olympiads: the
olympic games were celebrated at the full moon near the fummer folftice,
at the end of every fourth year, and the beginning of the fifth: the firſt of
them began 777 years before Chriſt.
1288 The building of Rome was a few years later, it is generally referred
to the
752 year before Chrift neither of the two laft mentioned epochs are
exactly and certainly determined.
1289 The year of Nabonaſſar is famous among aftronomers: the beginning
of it was on the 26 of february of the Julian year carried back to the 747
year before Chriſt: as this was then the first day of the Egyptian year, Ptolemy
in
СНАР. 14.
541
ASTRONOMY
in his Almageſt computes from it, and ſeveral writers after him, and Coper-
nicus among the reft; all reckoning by Egyptian years of 365 days each, the
moſt convenient of any for aftronomical calculations, as they confiſt of
whole days without fractions.
The year of the death of Alexander the great is another æra made uſe of
by Theon and Albatennius: it begins exactly 424 Egyptian years after the æra
of Nabonaffar. As for other epochs, as that of the begira or flight of Ma-
homet from Mecca to Medina, the ara of the Seleucida, that of Dioclefian or
the martyrs that ſuffered under his perfecution, and others now of little uſe,
they may be ſeen in books of chronology, and particularly in Scaliger de
emendatione temporum, & ifagog. Petavius and Strauchius.
1290 There are various opinions about the time of the year when the
world was created, fome will have it to have been in the ſpring, at the ver-
nal equinox; others, which feems to be the moſt generally received opinion,
contend for the autumnal equinox: to eſtabliſh this Strauchius brings no few-
er than ten arguments. Some writers have pretended to find the day and year
of the creation by aftronomical calculations; but in order to this they take
for granted certain poftulata without fufficient proof: thus, fome have ſup-
pofed the fun and moon and the orbits of thoſe luminaries at their creation
to have been in certain poſitions, wherein they are not found but after a great
number of years; and then by tables of their motions have calculated at what
time they were in fuch pofitions: Kepler a ſuppoſed the funs apogee at the
time of the creation to have been in o° of y, the point of the vernal equinox,
and finding that apogee in the year 1600 to have been in 19° 13′ 36″ of 11,
computes the creation to have been 3993 years before Chriſt, and ſuppoſes
it to have been when the fun was in o° of the point of the ſummer
folftice: from the fame principle Longomontanus b by fuppofing a diffe-
rent motion of the funs apogee, makes the creation only 3954 years be-
fore Chriſt. A like attempt to diſcover the time of the creation has been
made by a late author from fome of Bradley's obfervations of the fun and
moon: how likely any method of this kind is to be fuccefsful I leave to the
reader to judge.
The intervals between the birth of Abraham and the flood mentioned
§ 1233, are taken from Strauchius's chronology; but have been matter of
diſpute as may be feen there, p. 195. See also Shuckford's connection,
vol. 1. p. 273.
a Tab. Rudolphin. part 2. p. 42.
b Aftronom. Danic. Theoricor. 1. 1. c. 2 & 3.
3Z
CHAP.
542
BOOK 3
ASTRONOMY
2
CHAP. 15. OF COMETS.
1291 Of all the heavenly bodies there are none the courfes whereof are
apparently fo irregular as the comets: for they are found indifcriminately in all
parts of the heaven and move in all directions: and, though they be very
numerous, it is rare to find any two of them that have gone very nearly in
the fame track: one thing has been obſerved of them in general, that the
velocity of their motion increaſes as they draw nearer to the fun, and is re-
tarded as they recede to a greater diftance from that luminary.
1292 It has before been faid, § 618, 624, 637 and 641, that feveral
comets perform their revolutions round the fun, that they revolve in elliptic
orbits, that their orbits are in different planes, that their periodical times
are different, and that the motions of fome of them are direct, of others re-
trograde: this account of the comets is now generally acknowledged to be
true by the aftronomers of the preſent age, and is the refult of many exact
obfervations, and laborious calculations of the moderns: part of this doctrine
was received by ſome of the moſt ancient philofophers among the Greeks, of
the Italic and Pythagorean ſchools; for they held them to be ſo far of the
nature of the planets, that they had their periodical times of appearing, that
they were out of fight for a long time, while they were carried aloft at an
immenſe diſtance from the earth, but became viſible when they deſcended
into the lower regions of the air, being then nearer to us.
Theſe opinions were probably brought from Egypt, from whence the
Greeks fetched great part of their learning: the Egyptians are thought to
have borrowed their aftronomy from Chaldea: the ancient Chaldeans are faid
not only to have looked upon comets to be a kind of planets, that had perio-
dical motions, but alſo to have foretold their appearances; this laft was un-
doubtedly a vain boaſt of theirs, but is the lefs to be wondered at, as they pre-
tended to foretell earthquakes alſo: theſe predictions were probably founded
not upon any knowledge of the periodical times of comets, or any maxims
of true philofophy; but upon fome fallacious rules of judicial aftrology, to
which that nation was greatly addicted.
1293 Ariftotle, who mentions this doctrine of the ancient philofophers
about comets, was himſelf of another opinion: he maintained that the hea-
vens were unchangeable, not liable to generation or corruption: confequently
that comets, which he thought to be generated when they first make their
appearance, and to be deſtroyed when they can no longer be ſeen, could not
be reckoned among the heavenly bodies, but were only meteors or exhalations
raiſed
CHAP. 15.
543
ASTRONOMY
raiſed up into the upper regions of the air, where they blazed out for a while,
and diſappeared when the matter of which they were formed was conſumed ª.
1294 Seneca, a Roman philofopher who lived in the firft century of the
Chriſtian æra, mentions Apollonius of Myndus, a very careful obſerver of
natural cauſes to have been of the fame fentiments with the moſt ancient
Greek philofophers, with regard to comets. Seneca, had himſelf feen at leaſt
two comets, one in the reign of Claudius, the other in that of Nero; befides
that which he ſaw in his youth a little before the death of Auguftus, which
in one place he calls a comet, in another a prodigy: he manifeftly intimates
that he thought them above the moon; argues ſtrongly againſt thoſe who
imagined them to be meteors lifted up into the air by winds, or held fome
other abfurd opinions concerning them; and declares his belief that they
were not fires fuddenly kindled, but the eternal productions of nature.
The fame writer points out the only way to come at a certainty in this
matter; and that is by collecting a number of appearances of comets, in order
to diſcover whether they return periodically or not; for which purpoſe, ſays
he, one age is not ſufficient: and he goes on to prophecy, that the time will
come when the nature of comets and their magnitude will be demonſtrated,
and the routs they take, fo different from thoſe of the planets; and that
pofterity will wonder the preceding ages fhould be ignorant in matters ſo
plain and eaſy to be known b.
The cauſe of this ignorance is manifeſt enough; it was the great autho-
rity that Ariſtotle had among the aſtronomers and philofophers of later times;
fo great that his affertions were taken for demonſtrations: fo that even where
the ſtudy of aſtronomy flouriſhed, no body thought it worth the while to fet
down the motions of what that philofopher had pronounced to be nothing but
meteors cafually lighted up in the air, though they were found to be at a great
height, higher than the clouds, and ſubject to the diurnal motion which the
clouds are not; however, the appearance of comets being rare and uncommon,
fuperftitious fear laid hold on that circumftance and imagined they portended
great changes upon the earth, and diſaſters to mankind: that they were fore-
runners of war, peftilence, famine, earthquakes, deaths of great men and revo-
lutions in kingdoms and ſtates: agreably to this opinion, they were judged to
have different influences according to their different appearances; from whence
they had alſo different denominations: for fome were faid to be bearded,
fome hairy, fome to repreſent a beam, a fword or spear, others a target or
buckler; whereas the aftronomers of the prefent age acknowledge but one
fpecies of comets, and account for the different appearances of them from
}
a Meteor. 1. 1. c. 6 & 7.
b Senec. nat. kift. 1. 7.
3 Z 2
the
544
BOOK 3.
ASTRONOMY
the diverſity of their fituation with refpect to the fun and the earth: now had
they been believed by the ancients to be folid bodies, coeval with the folar
ſyſtem, whereof they make a confiderable part, they would no more have
been objects of fear than the rifing and ſetting of the reſt of the heavenly
bodies are; they would have excited no other fentiments in mankind than
what every other phenomenon in the univerſe ought to excite, admiration of
the infinite wisdom and power of the fupreme Being, manifefted in the
variety grandeur and perfection of the works of the creation.
1295 Tycho Brahe was the firſt among the moderns who reſtored comets
to their true places, in the planetary regions; for though after the revival of
learning in Europe, feveral comets had been before tolerably well obſerved by
Regiomontanus, Apian, Fabritius and others, yet they all thought them below
the moon: but Tycho, being provided with much better inftruments for obſerv-
ing the ſtars, than had been uſed by any aftronomer before, fet himfelf to obferve
the famous comet which appeared in 1577 with great diligence, and from
many careful obſervations found that it had na fenfible diurnal parallax, and
therefore was not only far above the limits of our air, but much higher than
the moon itſelf; as may be feen at large in his book de cometâ anni 1577.
1296 Though few comets have come fo near the earth as to have a diurnal
parallax, they are all fubject, in the fame manner as the planets are, to what
may be called annual parallax; that is, the revolution of the earth in her
orbit cauſes their apparent motion to be very different from what it would
be if they were viewed from the fun, or any fixed place: for example,
thofe comets that revolve according to the order of the figns, when they are
near diſappearing, in going towards their aphelions are retarded in their
motion, and become retrograde, when the earth is between them and the
fun; and their velocity increaſes when the earth is going into oppofition to
them: the reverſe to this happens to thoſe comets which revolve contrary
to the order of the figns; for fuch appear to go fafter than their real motion
carries them, when the earth is between them and the fun; flower, and
even retrograde, that is contrary to their former motion, when the earth is
going towards an oppofition. This fhews them not to be ſo diſtant as the
fixt ſtars, which are not ſubject to annual parallax: and as Hevelius ob-
ferves, is a proof of the earths revolution round the fun, for without fup-
pofing that, theſe motions of comets are inexplicable.
1297 After Tycho came Kepler, who, in his book de cometis, from obfer-
vations of the comets which appeared in 1607 and 1618, concluded that
comets move freely through the planetary orbs, with a motion not much dif-
ferent from a rectilinear one: he was followed by Hevelius an accurate ob-
ferver
CHAP. 15.
545
ASTRONOMY
ferver of the heavenly bodies, who found, by his own obfervations of two
comets that appeared in his time, that they were not fubject to diurnal
parallax: that calculations of their places made upon a fuppofition that they
moved in ftrait lines did not agree with their true places; but that their
orbits were concave towards the fun: and concluded that they moved in
parabolic trajectories a.
1298 At length the great comet in 1680 appeared, which, defcending out
of the immenſe regions of ſpace, almoſt perpendicular to the fun, with a pro-
digious velocity; afcended again in the fame manner from him, with a ve-
locity retarded as it had before been accelerated. The Royal obfervatories
at Paris and Greenwich were now built, and in the hands of very able aftro-
nomers, Caffini and Flamstead; who were both affiduous in obferving the
places of this comet: as were alfo Montanari, partly at Padua and partly at
Venice, Pontheus and others at Rome b, and ſeveral aftronomers in different
parts of Europe, by whom it was feen in the morning from the 4 to the 25
of november in its defcent toward the fun; and, after it had paffed its
pe-
rihelion, in the evening from the 12 of december to the 9 of march follow-
ing. The many exact obfervations made thereof enabled the great Newton
to diſcover that fo much of its orbit as could be traced out by the motion
of the comet while it was vifible, was as to fenfe a parabola, having the fun
in its focus; and that it was one and the fame comet that was ſeen all that
time d: indeed he once thought he found it deviate a little, about the end of
its appearance, from the parabolic trajectory towards the axis of the para-
bola; and thence concluded that it moved in an elliptic orbit, and computed
its period to be above 500 years e.
Though the motion of comets be known to be in ellipfes, they are cal-
culated as if they moved in parabolaes, for the eaſe of calculation: Newton
folved a very difficult problem, worthy of his genius, which teaches from
three places of a comet given, to find the parabola in which it moves f.
1299 Not long after, Dr. Halley having collected all the obfervations
of comets he could meet with, computed the orbits of 24 of them, upon a
fuppofition that they moved in parabolaes: but from the frequency of their
appearances thought it highly probable that they move in very excentric
elliptic orbits, and return after long periods of time. The aftronomical
elements of the motions of thoſe comets are fet down in the following table
a Hevel. prodrom. comet. p. 24. id. Hiftor. comet. p. 641, 659.
c Caffini, abrige de obfervat. fur le comete ann. 1680 & 1681.
b Mifcellanea Italica phyfico mathemat.
d Domenico Caffini imagined the comet
of 1680 was different from that of 1681: this was owing to his not allowing the motion of the earth.
e Newt. princip. p. 465, edit. Cantab. 1713.
•
f id. ibid p. 451.
raken
54.6
BOOK 3
ASTRONOMY
taken from Halley's fynopfis of the aftronomy of comets, a work that coſt
him an immenfe labour, and is deſervedly much eſteemed: it is tranflated
into French by Monnier, and an abridgment thereof publiſhed by De la Lande
with additions or remarks, and the hiſtory of the comet of 1759.
Comets
A. D.
1337
1472
5 20
8
15318 19 25
017 56
w
I 39
1532
20 27
032 36
1556 m 25 42
032
6 30/7
8
577
25 52
074 32 45
1580
18 57 20
64 40 0
A TABLE OF THE ELEMENTS OF COMETS.
| Afcending node | Inclin of orbit
Perihelion
O 1 "/
O
O
24 21 032 11
11 46 20
Perihelion Equat. time of perihel.
diſtance
"from the fun
08759
15 33 30
021 7
D. H.
040666 June 2 6 25 retrog.
54273 Feb. 28 22 23 retrog.
56700 Aug. 24 21 18 retrog.
50910 Oct. 19 22 12 direct
0
50 0
922
46390 Apr. 21 20 3 direct
018342 Oct. 26 18 45 retrog.
Nov. 28 15 o direct
19 5 50 59628
15858 7 42 30
6
4
4
ရာ 8 51 0109358
Sept. 27 19 20 direct
1590 m 15 30 40
29 40 40 m
1596 m 12 12 30 55 12
om
6 54 30
18 16 o
57661
Jan. 29
51293
Jan. 29 3 45 retrog.
July 31 19 55 retrog.
16078 20 21
017 2
2 16 0
58680
Oct. 16 3 50 retrog
1618 п 16 1 0 37 34
or
p
2 14
2 14 0
37975
O
Oct. 29 12 23 direct
1652 28 10
II 28 10 0 79 28
Y
28 1840
84750
п
1661 22 30 30 32 35 50
1664 21 14 0 21 18 30 2
Nov. 2 15 40 direct
25 58 40
44851
Jan. 16 23 41 direct
10 41 25
102575
Nov. 24 11 52 retrog.
1665 m 18 2 0:76 5
0
11 54 30
10649
Apr. 14 5 15 retrog
1672 27 30 30 83 22 10 8
16 59 30
69739 Feb. 20
8 37 direct
1677 m 26 49 10 79
3
15 2
17 37 5
28059 Apr. 26
o 37 retrog.
1680 % 2 2 0 60
0,60 56
22 39 30
00612 Dec. 8
6 direct
1682 21 16 30 17 56
0
2 52 45
58328 Sept. 4
7 39 retrog.
II
0
25 29 30
·
40 m
40
п
28 52 0
17 0 30
0%
3
051
1683 m 23 230 83 11
1684 28 15 065 48
1686 20 34 40 31 21
1698 27 44 15 11 46
↑
96015 May 29 10 16 direct
32500 Sept. 6 14 33 direct
69129 Oct.
Oct. 8 16 57 retrog.
The perihelion diſtance from the fun in the fifth column is in ſuch
as the diſtance of the earth from that luminary contains 100000.
parts
56020|July 3 2 50 retrog.
0 51 15
1300
CHAP. 15.
547
ASTRONOMY
1300 From comparing theſe elements together, it is plain that comets are
not comprehended within a zodiac as Caffini imagined, nor indeed are their
orbits diſpoſed in any order, but they move indifferently in all manner of di-
rections, as well retrograde as direct, through the regions of the planets:
this proves at once that the planets are not carried in folid orbs as the ancients
fuppofed; nor are they carried round by ſwimming in a vortex or whirlpool,
as Des Cartes and his followers imagined.
The comet of 1577 was remarkable for Tycho Brahe's diſcovering that it
had no parallax, and confequently was farther off than the moon: the Ari-
ftotelians difputed this matter, and Scipio Claramontius wrote a treatiſe a-
gainſt Tycho's affertion of no diurnal parallax. Ricciolus gives a detail of the
controverſy, which now no longer ſubſiſts.
1301 Halley, by comparing the elements in the foregoing table, concluded
that the comet in 1682 was the fame with that in 1607 and that in 1531:
that it had a period of 75 or 76 years; and ventured to foretell that it would re-
turn again about the year 1758: time has fince verified the prediction; and,
notwithſtanding what has been reported of the ancient Chaldeans and Egyp-
tians, I think we may fafely pronounce that an Engliſhman firſt of all men
foretold the return of a comet. The comet of 1661 ſeems to be the fame
with that of 1532, and to have its period in 129 years. From the equa-
lity of periods, and fimilitude of appearances, Halley thought that the
wonderful comet of the year 1680 was the fame that was ſeen in 1106
in the time of Henry I, that had been ſeen in the confulate of Lampadius
and Oreftes about the year 531, and in the 44 year before Chriſt, wherein
Julius Cæfar was murdered; and thence concluded that its period was 575
years: but Mr. Dunthorne a has endeavoured to ſhew from a MS. in Pembroke
Hall library, that the comet of 1 106 could not be the fame with that of 1680:
however, Mr. De la Lande b thinks the four appearances of this comet re-
marked by Halley ftronger proofs, than one obfervation flightly related, and
which might be very faulty.
1302 Following the ſteps of fo great a man as Dr. Halley, other aſtrono-
mers have computed the orbits of 25 other comets, the elements whereof
are ſet down in the following table, all taken from the Philofophical tranf-
actions, except the third comet from De la Caille's aftronomy, and the four
laſt from De la Landed. The times are reduced to the meridian of London,
and all before the year 1752 are old ſtyle as thoſe in Halley's table are.
a Phil. tranf. vol. 47.
↳ Additions a la theorie des cometes du Mr. Halley, p. 91. c pag. 236.
d Hiftoire de la Comete de 1759, P. 112. & Connoiffance des moumens celeftes 1762, & 1764.
A TABLE.
1
}
548
BOOK 3
ASTRONOMY
A. D.
D. H.
O
1264 July
1533 June 16
1593 July
6 8
om
19 30 2
8 13
38 m
1678 Aug. 16 14
3 m
1699 Jan.
3 8 22
19 o 036 30
544 035 49
14 14 15 87 58
11 40 0 3 4
21 45 35 69 20
A SUPPLEMENT TO HALLEY'S TABLE OF THE ELEMENTS OF COMETS.
Equated time of perihelion
Afcending node, Inclin. of orbit
"
Perihelion
O
021
Ъ 21 0
་
Perihelion
diſtance
"from the fun
Q
O
02 27 16
om 26 19
0
44500 direct
20280 retrog.
8911 direct
we
20 27 46
0123802 direct
0m 231
6
74400 retrog.
1702 Mar.
2 14 12
9 25 15 4 30
08
02 18 41 3
64590 direct
1706 Jan. 19 4 56
1707 Nov. 30 23 438
1718 Jan. 4 I 15
1723 Sept. 16 16 10
13 11 23 55 14
22 50 29 88
5
12 36 25
625
42686 direct
37
40
19 58 9
85904 direct
7 55 20 31
12
532
53 2
1 26 36
102565 retrog.
14 16 049 59 08
12 52 20
99865 retrog.
1729 June 12 6 36
1737 Jan. 19
1739 June 6
8 20m
16 22
10
0
Y
10 35 15 77 1 58
018 20 45
27 25 1455 42 44
22 16 53
406980 direct
25 550
22282 direct
12 38 40
67358 retrog.
1742 Jan. 28
1742 Dec. 30 21 15
4 21
421
5 34 45 67 4 11m
7 33 44
76555 retrog.
8 10 482 15 50
2 58 4
83811 direct
1743 Sept. 9 21 16
5 16 25 45
1744 Feb. 19
1747 Feb. 17
1748 Apr. 17 19 25 m
1748 June 7 I 248
8 178
11 45 2
5 16 25 45 48 21 ↑
15 45 20 47
6
33 52 52157 retrog.
8 36
17 12 55
22206 direct
26 58 27 77 56 55 %
22 52 16 85 26
10 5 41
229388 retrog.
57 m
57m
5
50 50
840663|retrog.
4 39 43 56 59
3
6 9 24
9 24
65525 direct
1757 0. 21
1759 Mar. 12 13 508
1759 Nov. 27 2 19
1759 Dec. 16 12 41
1762 May 28 15 18
7 55m
4 12 50 12 50 202
2 58
O
33754 direct
23 45 35
19 39 24
17 40 15 m
78 59 22
3 8 10
23 24 20
584903 retrog.
79851 direct
18 56 19
4 37 23
19 2 48
96193 retrog.
#
19 23
0184 45 0
15 14 0
101240 direct
1303 By comparing theſe elements with thofe in Halley's table and with one
another, none of theſe comets (beſides the firſt in 1759, which was the fame
with thoſe of 1682, 1607 and 1531, in Halley's table) appears to be the
fame with any other in either of the tables, except perhaps the comets of
1264 and 1556, or thoſe of 1596 and 1699 fhould be the fame. From
hence we may conclude the number of comets to be very great: nor is it at
all
+
1
page 549.
90.
Book III.
Mar 5
Feb:54
Jan25
Orbit
of
Jan 5
the
Nov:17
Dec:29
Nov.21
Nov 25
Decan
Decra
The
Sun.
123.
}
Earth
A
B
119.
K
M
C
120.
121.
122.
124.
เน
AINS
C*H A P. 15.
549
ASTRONOMY
all unlikely, from the immenfe interval between the orbit of ſaturn and the FIG.
neareſt fixt ſtars, that many of them have not deſcended into the plane-
tary regions, fince they have been looked upon as celeſtial bodies, and ob-
ſerved accordingly: befides, it may often happen that a comet may finish its
whole period without being obſerved by us, on account of the unfavourable
fituation of the earth in her orbit when the comet is near its perihelion: thus,
if the comet be then behind or before the fun, or nearly fo, it muſt be above
our horizon in the day time, and conſequently invifible, except the fun
ſhould at that time be in a total eclipſe; for then the comet might be ſeen
near the fun, as well as the ſtars and planets are: and this caſe is ſaid to have
happened, for Seneca relates from Pofidonius, that a comet was ſeen when
the fun was eclipſed, which had before been invifible by being near that
luminary a.
1304 There is a manuſcript b in the library of the Univerſity of Cambridge
wherein fome account is given of a comet that appeared in the ſpring of
the year 1299; Mr. Dunthorne, computing from what is therein related
(though it be not fufficient to determin the elements with any accuracy) finds
the afcending node to have been about 25° of ¤, the inclination of its orbit
about 20°, the place of the perihelion (wherein the comet was about the begin-
ning of february) near the end of or the beginning of 2, its perihe-
lion diſtance a little greater than the mean diſtance of the earth from the
fun, and that its motion was retrograde: all theſe elements agree fo well
with thoſe of the comet of 1664 that he thinks it was probably the
ſame comet; if it was, the period thereof is about 365 years. This receives
ſome confirmation from the hiſtory of comets; for, though we meet with no
account of any comet in 934, one period backwards, we find there was
a comet feen in 570, nearly at the diſtance of two periods, as there was alfo
one in the year 204, at the diſtance of a third period. From what
was faid § 1303, it is manifeft that a comet feen in one of its periods may
not be viſible in another period.
C
1305 More comets are ſeen in the hemiſphere towards the fun, than in the
oppofite hemifphere, the reafon whereof will eafily appear from the 119 119
figure, wherein s reprefents the fun, E the earth, the circle ABCD the
ſphere of the fixt ſtars; and, becauſe comets do not either reflect light enough
to be viſible, or emit tails confpicuous enough to be taken notice of by us till
they are come within the planetary regions, commonly a good way within
a Nat. queft. 1. 7.
c See Halley's table.
b Judicium de ftella comata a magiftro Petro Lemonienfi canonico eboracenfi.
4 A
the
550
BOOK '3
ASTRONOMY
FIG. the fphere of jupiter, let KLMN be a ſphere concentric to the fun at ſuch a
119 diſtance from him that no comet can be ſeen by us till it comes within the
faid diſtance: through E draw the plane B D perpendicular to s E which will
divide the ſphere KL MN into two portions L M N and NKL, and the ſphere
ABCD into two hemifpheres one of which BCD is towards the fun, the other
DAB is oppofite thereto: now it is manifeft the ſpherical portion LMN
which is in the hemifphere BCD towards the fun is larger than the portion
NKL in the hemiſphere DAB oppofite to him, and confequently more comets
will appear in the hemifphere B CD than in the hemifphere DAB.
1306 It has already been faid that the orbits of comets as well as thoſe of
the planets are ellipfes; it muſt be added that the elliptical orbits of the co-
mets differ very much from one another; whereas, mercury excepted, there
is very little difference between the orbits of the planets, as to their excen-
tricities or the pofitions of their planes: comets differ very much from each
other in both theſe particulars; for the planes of the orbits of fome of them are
almoſt perpendicular to thofe of others, and their ellipfes are of very different
forms, fome being much wider than others: thus, the ellipfis of the comet
of 1680 was much narrower than any other hitherto obferved. There is alſo
a greater inequability in the motion of the comets than in that of the planets:
the velocity of comets is incomparably greater in their perihelions than in
their aphelions; the motions of the planets are but a very little ſwifter in the
former fituation than in the latter. See book 2. chap. 4 & 7.
It is obvious to remark, that if a comet were to continue to move with
the fame velocity, its apparent motion would be ſwifter when it came nearer
the earth; for the arc through which it goes in any given time, like all other
objects, appears larger the nearer it is to the eye.
The greateſt apparent velocity of a comet mentioned any where is that
of the comet in 1472, obferved by Regiomontanus to have gone through 40
degrees of a great circle in 24 hours.
1307 The head of a comet, to the eye unaffifted with glaffes appears fome-
times like a cloudy ftar, fometimes fhines with a dull light like that of the
planet faturn; fome comets have been faid to equal, fome to exceed in bright-
nefs ſtars of the firſt magnitude, fome to have furpaffed jupiter and even
venus; and to have caft a fhadow, as § 727, venus was faid fometimes to do.
The head of a comet feen through a good teleſcope appears to confift of
a folid globe and an atmoſphere that furrounds it: the folid part is frequent-
ly called the nucleus, a latin word that fignifies the kernel of a nut: through
a teleſcope, the nucleus is eaſily diſtinguiſhed from the coma or hairy ap-
pearance of the atmoſphere.
A comet
CHAP. 15:
551
ASTRONOMY
A comet is generally attended with a blaze or tail, whereby it is diftinguiſhed FIG.
from a ſtar or planet; as it is alfo by its motion. Sometimes the tail only
of a comet has been vifible at a place where the head has been all the while
under the horizon; fuch an appearance is called a beam.
1308 That comets are opake bodies enlightened by the fun as the planets are
is a matter about which aſtronomers are now pretty well agreed: Hevelius,
in a large work wherein he produces the opinions of various authors upon
this ſubject, mentions fome who were of the fame opinion with himſelf,
that comets were fo far tranfparent as to let enough of the funs light pafs
through them to form their tails: he gives pictures of comets of various
fhapes, as they are deſcribed by hiftorians to have been like a fword, a buck-
ler, a tun, &c. theſe are drawn by fancy only, from the defcription in words:
what is more to the purpoſe, he gives alſo pictures of fome comets, engraved
by his own hand from the views he had of them through a very long and
excellent teleſcope; in theſe we find changes in the nucleus, the atmoſphere,
and the tail of the fame comet: the nucleus of the comet of 1661, which in
one obfervation appeared as one round body, as it is reprefented in fig. 121, 121
in ſubſequent views feemed to confiſt of ſeveral ſmaller ones feparated one
from another, as in fig. 122: the atmoſphere furrounding the nucleus view- 122
ed at different times varied in the extent thereof, as did alfo the tail in
length and breadth.
Sir Ifaac Newton, who was of opinion that comets are opake bodies en-
lightened by the fun, obferved, in confirmation thereof, that if a comet be
ſeen in two points of its orbit that are at equal diſtances from the earth, but
at unequal diſtances from the fun, it always fhines brighteſt when in the
point neareſt to the fun ª.
1309 The nucleus of the comet of 1618, is faid a few days after coming
into view to have broken into three or four parts of irregular figures: one ob-
ſerver b compares them to ſo many burning coals, fays they changed their ſitu-
ation while he was looking at them, as when a perſon ſtirs a fire; and a few
days after were broken into a great number of ſmaller pieces. Another
account of the fame is, that on the 1 and 4 of december the nucleus ap-
peared to be a round folid luminous body, of a dufky lead colour, larger
than any ſtar of the first magnitude; on the 8 of the fame month was brok-
en into three or four parts of irregular figures; and on the 20 was changed
into a cluſter of ſmall ſtars.
1310 If comets revolve in fuch large orbits during fuch long periods as
we have now reaſon to believe, it is not probable they ſhould confiſt of ſe-
a princip. p. 443. b Wendelinus apud Hevel, cometograph, P. 342. c Cyfatus ef. eund. p. 341-
4 A 2
veral
552
BOOK 3.
ASTRONOMY
veral maffes compacted together with a tranſparent fluid interfperfed, as
Hevelius imagined, in order to make good his explanation of the phenome-
na of the tails: the apparent changes in the nucleus may be only on the fur-
face: comets may be fubject to ſpots as the planets are, and the vaſtly different
degrees of heat they go through may occafion great and ſudden changes, not
only in their ſurfaces, but even in their internal frame and texture. Newton
places all theſe apparent changes to the atmoſphere that environs them:
this muſt be very denſe near the nucleus, and have clouds floating therein;
it was his opinion that the changes mentioned may all be in the clouds,
not in the nucleus of the comet a.
1311 Comets are of different magnitudes: the magnitude of a comet, may
be conjectured, from its apparent diameter and brightneſs: thus, the head
of a comet, when of the fame brightneſs and apparent diameter with fa-
turn, may be judged to be nearly of the fame magnitude with that planet b:
but this muſt be uncertain; becauſe we cannot be affured that the heads of
comets reflect the light of the fun in the fame manner as the folid globes of
the planets do.
If the parallax of a comet be known, the diſtance thereof from the earth
may be found by § 143 and 147: the horizontal parallax of the comet of 1577
on november 13 was determined by Tycho to be about 16 minutes; and the
diſtance from the earth 210 femidiameters of the earth: on the fame day
the apparent diameter of the comet was meaſured by him 7 minutes: and
from the diſtance and apparent diameter, § 148, the true diameter was com-
puted to be to the diameter of the earth as 3 is to 14.
atmoſphere of the comet that was then meaſured.
It was the
Hevelius, from the parallax and apparent magnitude of the head of the
comet of 1652 on december 20, computed the diameter thereof to be to
that of the earth as 52 to 100, a little more than halfe. By the fame me-
thod, he found the true diameter of the head of the comet of 1664 to be at
one time 12 femidiameters of the earth, at another time not much above 5
femidiameters. That the head of a comet appears lefs the farther it is from
the earth is obvious: befides this apparent change, there is alſo a real one in
the dimenfions of the head of the fame comet; for when near the fun the
atmoſphere is diminiſhed by the heat raifing more of it into the tail; whereas
at a greater diſtance the tail is diminiſhed and the head enlarged f.
a princ. pag. 444· bib. pag 441,
c Tycho Brahe de cometa anni 1577.1. 2. p. 202. d p. 336.
e He found its horizontal parallax december 23, to be very near 30', and with a large braſs quadrant ob-
ferved its apparent diameter the fame day 25′ or 26′, almoſt equal to that of the moon in apogee.
f Newton p. 473.
t
The
CHAP. 15.
553
ASTRONOMY
The diameter of the head or atmoſphere of the comet of the year 1682,
as meaſured by Flamstead a was two minutes, the diameter of the nucleus
only 11 or 12 feconds: the diameter of the atmoſphere is often ten or fifteen
times as great as that of the nucleus b: this, according to Newton and other
philofophers of the preſent age, furniſhes matter for thofe fplendid tails
wherewith we often fee comets attended, and by which as well as by their
motion they are diſtinguiſhed from the ſtars and planets. Hevelius computed
the diameter of the nucleus of the comet of 1661 and alſo of that of 1665
the beginning of their appearances to be leſs than a tenth part of the diame-
ter of the earth. Cyfatus makes the true diameter of the head of the comet
of 1618 about a tenth part of the diameter of the earth.
in
1312 There are ſome eclipſes of the fun recorded in hiſtory which cannot
be verified by calculation from tables of the fun and moon: fome have thought
thoſe darkneſſes may have been caufed by the interpofition of comets between
the fun and the earth: the eclipfes of the fun mentioned by Herodotus, 1.
7.
c. 37. & l. 9. c. 10. are thus accounted for, as is alſo the eclipſe that hap-
pened a few days before the death of Auguftus, mentioned by Dion; it is
obfervable that Seneca faw a comet the fame year.
Some comets, from their apparent magnitude and diſtance confidered to-
gether, have been judged to be much larger than the moon, and even equal
in magnitude to fome of the primary planets: a globe of that ſize ſo much
larger than the moon is, might cover the fun, and caufe an eclipfe. We
read in hiſtory of comets that have appeared as large as the fun, if ſuch an
one near its perigee were to come between the fun and our earth, it would
eclipſe him for a time.
Some have thought the darkneſs at our Bleffed Saviours crucifixion might
be cauſed by a comet coming then between the earth and the fun d; this fup-
pofition does not detract from the miracle; the divine interpofition would be as
neceffary to order that thoſe two events ſhould fall out exactly at the ſame
time as it would be to caufe fuch darknefs by any other extraordinary means.
1313 Various have been the opinions of philofophers concerning the tails
of comets: that the tails of comets depend upon the fun is acknowledged by
all, for this plain reafon, that they are always turned from that luminary;
but how they are caufed by the fun is much controverted: Apian, Tycho
Brake and others thought the tail was produced by the funs rays tranfmitted
through the nucleus of the comet, which they fancied tranfparent, and
a Newton, pag. 441.
b ib. pag. 442.
c Seneca, N. 2.1. 7. c. 15. paulo ante Achaicum bellum
cometes effulfit non minor fole. d Hevel. cometogr. p. 540. Freret, reflexions fur un ancien phenomene
celefte au temps d'Ogyges, memoires de literature, vol. 19. p. 357-
was
554
BOOK 3
ASTRONOMY
was there refracted as in a lens of glafs, fo as to form a beam of light behind
the comet; but this cannot be the cafe; as well becauſe the figure of a comets
tail does not anſwer to fuch a refraction, as that fuch refracted light would
not be ſeen by an eye placed fidewife to it, unleſs it fell upon ſome reflecting
ſubſtance denſer than the circumambient ether.
1314 Another opinion is that of Des Cartes and his followers, who would
have the tail of a comet to be owing to the refraction of the light from its head
to the eye of the ſpectator: if this were ſo, the planets and principal fixt ſtars
muſt have tails alfo; for the rays of them pafs through the fame medium
before they reach our eyes, as light from the comets does.
1315 It was the opinion of Newton that the tail of a comet is a very thin
vapour which the head fends out by reafon of its heat: that it afcends
from the fun juſt as ſmoak in a chimney does from the earth: that as the
aſcent of ſmoak is owing to the rarefaction of the air wherein it is entang-
led caufing fuch air to afcend and carry the fmoak up with it, fo the funs
rays acting upon the coma or atmoſphere of a comet do by reflection and re-
fraction heat the fame: that this heated atmoſphere heats, and by heating
rarifies the matter of the ether that is involved therein; and that the ſpecific
gravity with which ſuch ether tends to the fun is ſo diminiſhed by this rare-
faction, that it will now afcend from the fun by its relative lightneſs, and
carry with it the reflecting particles whereof the comets tail is compofed ª.
Though the immenfely large tails of fome comets feem to require a great
quantity of matter to produce them, this is no objection to the foregoing
folution; for every days experience fhews what a prodigious quantity of
fmoak is produced from a very ſmall quantity of wood or coal; and Newton
has demonſtrated that a cubic inch of our air, equally rarified with the air at
the diſtance of a femidiameter of the earth from its ſurface, would fill all
the planetary regions to the orbit of faturn and far beyond it b.
1316 A fourth opinion is that of Mairan, that the tails of comets are formed
out of the luminous matter whereof the atmoſphere of the fun confiſts, men-
tioned § 762: this is fuppofed to extend as far as the orbit of the earth; and
to furniſh matter for thofe northern lights called the aurora borealis: Mr.
De la Lande is for joyning the two laſt mentioned opinions together, in
order to account for the phenomena of the tails of comets: he thinks
part of the vapour which forms them ariſes out of the atmoſpheres of the co-
mets rarified by heat, and is puſhed forward by the force of the light ſtreaming
from the fun; and alfo that a comet paffing through the funs atmoſphere is
drenched therein, and carries away fome of it.
a princip. I. 3. P. 472.
bibid p. 479.
c additions a la theorie des cometes, p. 102.
1317
CHAP. 15.
555
ASTRONOMY
}
a:
1317 The laſt ſolution I ſhall mention of this appearance is that of Mr. FIG.
Rowning, he objects to Newton's account, that it can hardly be ſuppoſed poffi-
ble the thin vapour of the tail fhould go before the more folid body of a co-
met, when the motion thereof is fometimes fo extreamly ſwift as that of ſome
of the comets is ſaid to be, after the rate of above 600 miles in an hour 2: he
therefore fuppofes the atmoſphere of every comet to extend every way round
as far as the tail reaches; and that the part of it which makes the taikis dif
tinguiſhed from the rest by the rays of light from the fun being refracted ſo as
to fall thick upon the part of the atmoſphere which goes before the comet in
its progrefs along its elliptic orbit; the greateſt objection to it, is the im-
menſe largeneſs of the atmoſpheres that muſt now be fuppofed, to account
for the length of the tails of fome comets, which have been ſaid to meaſure
above 200 femidiameters of our earth..
13 18 As the tail of a comet is owing to the heat of the fun, it grows longer
as the comet approaches near to, and ſhortens as it recedes from that lumi-
nary: if the tail of a comet were to continue of the fame length, it would
appear longer or ſhorter according to the different views of the fpectator;
for, if his eye be in a line drawn through the middle of the tail lengthwife,
or nearly fo, the tail will not be diſtinguiſhed from the rest of the atmo-
ſphere, but the whole will appear round: if the eye be a little out of that
line, the tail will appear fhort, as in fig. 120; and it is called a bearded comet 120
when, the tail hangs downward towards the horizon as in that figure: if the
tail of a comet be viewed fidewife, the whole length thereof is feen: it is
obvious to remark that the nearer the eye is to the tail the
the length thereof appear.
greater will
The tails of comets often appear bent, as in fig. 123, 124: this is owing 123
to the refiftance of the ether, which though extreamly fmall, may have a fen- 124
fible effect upon fo thin a vapour as the tails conſiſt of: this bending is ſeen
only when the earth is not in the plane continued of the orbit of the comet,
when that plane paffes through the eye of the fpectator, the tail appears 121
ftrait, as in fig. 121, 122.
Longomontanus b mentions a comet that in 1618 december 10, had a tail
above 100 degrees in length; this comet muſt then be very near the earth:
the tail of a comet will at the fame time appear of different length in diffe-
rent places; according as the air in one place is clearer than in the other:
it need not be mentioned that, in the fame place, the difference in the eyes
of the ſpectators will be the caufe of their diſagreeing in their eſtimate of
the length of the tail of a comet.
a Hevel. p. 701.
b apud Hevel. p. 519.
122
1319
556
BOOK 3
ASTRONOMY
1319 Hevelius is very particular in telling us that he obſerved the comet
of 1665 to caſt a ſhadow upon the tail, for in the middle of the length there-
of there appeared a dark lineª: it is ſomewhat ſurpriſing that Hook ſhould
be poffitive in affirming on the contrary, that the place where the ſhadow of
that comet ſhould have been, if there had been any fhadow, was brighter
than any other part of the tail: he was of opinion that comets have fome
light of their own; his obfervations were made in a hurry; he owns they
were ſhort and tranfitory b: Hevelius's was made with fo much care, that
there is more reaſon to depend upon them: Dom. Caffini obferved in the tail
of the comet of 1680 a darkneſs in the middle of the tail: the like was taken
notice of by a curious obferver in the tail of the comet of 1744.
1320 The analogy between the periodical times of the planets and their
diſtances from the fun diſcovered by Kepler and mentioned § 914, takes place
alfo in the comets: in confequence of this, the mean diſtance of a comet from
the fun may be found by comparing its period with the time of the earths re-
volution round the fun: thus, the period of the comet that appeared in 1531,
1607, 1682 and 1759, being about 76 years, its mean diſtance is found by
this proportion; as I the fquare of 1 year the earths periodical time is to
5776 the fquare of 76 the comets periodical time; fo is 1000000 the cube of
100 the earths mean diſtance from the fun, to 5776000000 the cube of the
comets mean diſtance: the cube root of this laſt number is 1794, the mean
diſtance it ſelf in fuch parts as the mean diſtance of the earth contains 100.
If the perihelion diftance of this comet 58 be taken from 3588 double the
mean diſtance, we ſhall have the aphelion diſtance 3530 of fuch parts as
the diſtance of the earth contains 100; this is a little more than 35 times.
the diſtance of the earth from the fun: by a like method the aphelion
diſtance of the comet of 1680 comes out 138 times the mean diſtance of
the earth from the fun, fuppofing its period to be 575 years: fo that this
comet in its aphelion goes to more than 14 times the diſtance from the fun
that faturn does.
1321 There are three comets, thoſe of the years 1680, 1744, 1759, that
deſerve to have a farther account given of them: the comet of 1680, befides
what was ſaid of it § 1298, was remarkable for its very near approach to the
fun; ſo near that at its perihelion it was not above a fixth part of the diame-
ter of that luminary from the furface thereof: Newton made a calculation of
the heat it muſt then have fuftained, and found it near 2000 times as great as
that of red hot iron: the calculation is founded upon this principle, that the
heat of the fun falling upon any body at different diſtances is reciprocally as
a cometograph p. 898.
b cometa, or remarks about comets.
1
the
CHAP. 15.
557
ASTRONOMY
the ſquares of thoſe diſtances; this is true cæteris paribus, as was fhewn in the FIG.
introduction § 88: but it may be obſerved, that the effect of the heat of the
fun upon all bodies near our earth depends very much upon the conſtitution of
thoſe bodies, and of the air that furrounds them: fuch bodies as abound with
fulphureous particles are heated ſooner than others: there is in our air ſome-
times more fire than at other times: and there is more fire in the atmoſphere
near the earth than in the upper regions of it; how otherwiſe comes it to pafs
that fnow will lye unmelted upon the top of an high mountain when it is
hot weather in the valley near the foot of it. The comet in queſtion cer-
tainly-acquired a prodigious heat, but I cannot think it came up to what the
calculation makes it: the effect of the ſtrongeſt burning glaſs that has ever
been made uſe of was the vitrification of moſt bodies placed in the focus;
what would be the effect of a ſtill greater heat we can only conjecture; it
would perhaps fo difunite the parts as to make them fly off every way in
atoms.
This comet, according to Halley, in paffing through its fouthern node,
came within the length of the funs femidiameter of the orbit of our earth; had
the earth been then in the part of her orbit neareſt to that node of the comet
their mutual gravitation muſt have cauſed a change in the plane of the orbit
of the earth, and in the length of our year: he adds that if fo large a bo-
dy with fo rapid a motion as that of this comet near its perihelion were to
ſtrike againſt our earth, a thing by no means impoffible, the ſhock might
reduce this beautifull frame to its original chaos.
Fig. 123, tak-
123
en from Newton's principia, repreſents ſo much of the trajectory of this
comet as it paſſed through while it was viſible to the inhabitants of our earth,
in going to and returning from its perihelion: it ſhews alſo the tail, as it ap-
peared on the days mentioned in the figure: the tail, like that of other co-
mets, increaſed in length and brightneſs as it came nearer to the fun; and
grew ſhorter and fainter as it went farther from him and from the earth,
till that and the comet were too far off to be any longer viſible.
Euler computes the orbit of this comet from three of Flamsteed's obſerva-
tions taken near together, compared with a fourth taken at ſome diſtance
from the other three, and thence determines the periodical time to be a little
more than 170 years. It ſeems ſomething furprizing that from the fame ob-
ſervations that were uſed by Newton and Halley he ſhould bring out a pe-
riod fo very different from what thofe great men had determined; but it is
the leſs to be wondered at, if we confider how ſmall a portion of the comets
orbit lay between the moſt diſtant places uſed in this computation, or indeed
that could be had for that purpoſe; ſo ſmall that the form of the ellipfis
4 B
cannot
558
BOOK 3
ASTRONOMY
cannot be found with any precifion by this method, except the comets pla-
ces were more exactly verified than is poffible to be done a: and that he does
not pretend to confirm his determination of the period by pointing out and
comparing together any former appearances of this comet, a method which
Newton recommended as the only one whereby the periodical times and
tranfverfe diameters of the orbits of comets can be accurately determined.
1322 I muſt not conclude this account without mentioning that Whiston b,
who from Flamsteed's meaſure of its apparent diameter concluded the nu-
cleus of this comet to be about ten times as big as the moon, or equal to a
fourth part of our earth, attributes the univerfal deluge in the time of Noah
to the near approach thereof: his opinion was that the earth paffing through
the atmoſphere of the comet attracted therefrom great part of the water
of the flood: that the nearness of the comet raiſed a great tide in the ſubter-
raneous waters, ſo that the outward cruft of the earth was changed from
ſpherical to oval; that this could not be done without making fiffures or
cracks therein: that through theſe fiffures the fubterraneous waters were forced,
by the hollow of the earth being ſo changed into a lefs capacious form : that,
along with the water thus fqueezed up upon the furface of the earth, much
flime or mud would rife; which, together with the groffer parts of the co-
mets atmoſphere would, after the fubfiding of the water partly into the fif-
fures and partly into the lower parts of the earth to form the fea, cover all
over to a confiderable depth the antidiluvian earth: thus he accounts for trees
and bones of animals being found at very great depths in the earth.
He alſo held that before the fall the earth revolved round the fun in the
plane of the ecliptic, keeping always the fame points of its furface towards
the fame fixt ſtars: by this means, as every meridian would come to the fun
but once in a whole revolution, a day and a year were then the fame: but
that a comet ſtriking obliquely upon the earth gave it the diurnal rotation.
That the antidiluvian year confifted of 360 days; but that the additional
matter depofited upon the earth from the atmoſphere of the comet at the
flood, fo retarded the revolution thereof round the fun, that it is not now
performed in less than 365 days and about a quarter.
The fame comet he thought would probably, coming near the earth after
being heated to an immenfe degree in its perihelion, be the inftrumental caufe
of that great cataſtrophe, the general conflagration, foretold in the facred
writings, and from ancient tradition, mentioned by heathen writers.
1323 The comet of 1744 was feen by fo many perfons now living, and
made fo remarkable an appearance, that it will be very proper to give a more
a Euler fays they fhould be had to feconds.
b theory of the earth.
particular
CHAP. 15.
559
ASTRONOMY
particular account thereof: it was firſt ſeen at Lauſanne in Switzerland, de-
cemb. 13, 1743 N.S; from that time it increaſed in brightneſs and magnitude as
it was coming nearer to the fun: its orbit was found to differ fo little from a
parabola, that its period muſt be very long, even of many centuries: there is
no comet in Halley's catalogue the elements whereof are at all like thoſe of this
cometa. The diameter of it when at the diſtance of the ſun from us, mea-
fured about one minute; this brings it out equal to three times the diameter
of our earth: it came fo near mercury that, if its attraction were proportio-
nal to its magnitude, it was thought probable it would have diſturbed the
motion of that planet b.
Mr. Betts of Oxford, from fome obfervations made there and at Lord
Macclesfield's obfervatory at Sherburn, endeavoured to compute the longeſt
axis of the orbit, in order to find the period of this comet; but the axis came
out ſo near to infinite that, though this fhewed the period to be a very long
one, he deſpaired of finding out the length thereof, except he could procure
ſome obſervations made after the perihelion: thoſe he had enabled him to ſettle
the other elements fo exactly, that its places computed from them differed
only a few feconds from the obfervations: he found the nodes of this comet
were within half a degree of the nodes of mercury; but that there was the dif-
ference of above a week between the times of thoſe bodies coming to their
reſpective nodes: computing their heliocentric conjunction, when they were
neareſt to each other, he found the comet was then diftant from mercury a
fifth part of the diſtance of the earth from the fun, and was almoſt twice as
near to the fun as mercury was; and thence concludes the comet could have
no fenfible effect upon the motion of that planet: he judged the comet to
be in magnitude at least equal to our earth. He fays that in the evening
of january 23 this comet appeared exceeding bright and diſtinct and the di-
ameter of its nucleus nearly equal to that of jupiter; its tail extended above
16 degrees from its body, and was in length, fuppofing the funs parallax 10”,
above 23 millions of miles c. Dr. Bevis, in the month of may 1744,
made four obſervations of mercury, and found the places of that planet
calculated from correct tables differed fo little from the places obferved, as
to fhew the comet had had no influence upon mercury's motion d.
. The nucleus, which had before been always round, on the 11 of feb-
ruary appeared oblong, in the direction of the tail, and feemed divided
into two parts, by a black ftroak in the middle; one of the parts had a fort
of beard brighter than the tail; this beard was furrounded by two unequal
dark ſtroaks that feparated the beard from the hair of the comet: theſe odd
b id. ibid. p. 153. a pbilof, tranf n. 474. d ibid.
a Euleri, theoria mot. planet, et comet. p. 169.
4
B 2
phe-
560
BOOK 3.
ASTRONOMY
FIG. phenomena diſappeared the next day, and nothing was feen but irregular ob-
fcure fpaces like fmoak, in the middle of the tail; and the head reſumed its
natural form: february 15 the tail was divided into two branches, the eaſtern
part about 7 or 8 degrees long, the weſtern 24: on the 23 the tail began to
be bent: it fhewed no tail till it was as near to the fun as the orbit of mars:
the tail grew longer as it approached nearer to the fun: the tail at its great-
eft length was computed to equal a third part of the diſtance of the earth
from the fun. This account taken from the memoires of the academy of
ſciences of 1744, confirms Newton's opinion, that the apparent changes in
the nucleus of a comet are owing to changes in the atmoſphere thereof.
124 Fig. 124 is a view of this comet taken by an obſerver at Cambridge: I re-
member that in viewing it I thought the tail feemed to fparkle, or vibrate
luminous particles, Hevelius mentions the like in other comets; and that their
tails lengthen and ſhorten while we are viewing them 2: this is probably
owing to the motion of our air.
1324 The comet of 1759 did not make any confiderable appearance by
reafon of the unfavourable fituation of the earth all the time its tail might
otherwiſe have been confpicuous, the comet being then tco near conjunction
with the fun to be ſeen by us; but deferves our particular confideration as it
was the firſt that had ever had the time of its return foretold. Halley, after
he had made his table of comets, found fuch a fimilitude in the elements of
thofe of 1531, 1607 and 1682, that he was induced to believe them to be re-
turns of the fame comet in an elliptic orbit; but as there was fuch a difference
in their periodical times and inclinations of their orbits as ſeemed to make
againſt this opinion, and as the obfervations of the first of them in 1531 by
Apian, and of the fecond in 1607 by Kepler were not exact enough to deter-
min fo nice a point, when he firſt publiſhed his fynopfis in 1705, he only men-
tioned this as a thing very probable, and recommended it to poſterity to watch
for the coming again thereof about the year 1758. Afterwards looking over
the catalogue of ancient comets, and finding three others at equal intervals
with thoſe now mentioned, he grew more pofitive in his former opinion:
and, knowing a method of calculating with eafe motion in an elliptic orbit
how excentric fo ever it be, inſtead of the parabolic orbit which he had given
for the comet of 1682, he fet about adapting the plane of that orbit to an ellip-
fis of a given ſpecies and magnitude, having the fun in one of its focuſes, ſo as
to tally with the obfervations of that comet made by Flamsteed with great
accuracy by the help of a very large fextant: he likewife corrected the places
of the comet of 1531 from Apian, and thofe of the comet of 1607 from
a cometograph. p. 513, 519.
Kepler
·CHAP. 15.
561
ASTRONOMY
Kepler and Longomontanus, by rectifying the places of the ftars they had
made uſe of, and found thoſe places agree as well with the motion in ſuch
an ellipfis as could be expected from the manner of obſerving of thoſe aftro-
nomers, and the imperfections of their inftruments. The greatest objection
to this theory was fome difference in the inclinations of the orbits, and that
there was above a years difference between the two periods, the comet of
1531 was in perihelion auguft 24, that of 1607 october 16, and that of 1682
ſeptember 4; fo that the firſt of theſe periods was more than 76, the latter
not quite 75 years: to obviate this, he reminds his readers of an obfervation
made by him of the periodical revolution of faturn having been at one time
about 13 days longer than at an other time; occafioned, as he ſuppoſed, by
the near approach of faturn and jupiter, and the mutual attraction or gravi-
tation of thoſe planets; and obſerves that in the fummer of the year 1681,
the comet in its defcent was for fome months fo near jupiter that its gravi-
tation towards that planet was a goth part of its gravitation towards the
ſun ;
this he concluded would cauſe a change in the inclination of its
orbit, and alſo in the velocity of its motion; for by continuing longer near
the planet jupiter on the fide moft remote from the fun, its velocity would
be more increaſed by the joint forces of both thoſe bodies, than it would be
diminiſhed by thofe forces acting contrary ways, when on the fide next the
fun where its motion was ſwifter: the projectile motion being thus increaf-
ed, its orbit would be enlarged and its period lengthened; fo that he thought
it probable it would not return till after a longer period than 76 years, about.
the end of 1758, or the beginning of the next year.
As Halley expreffed his opinion modeftly, though clearly enough, that this
comet would appear again about the end of 1758, or the beginning of the
following year; Mr. De la Lande pretends he muſt have been at a loſs to
know whether the period he foretold would be of 75 or of 76 years, that he
did not give a decifive prediction as if it had been the refult of calculation, and
that by confidering the affair in ſo looſe a manner as Halley did, there was a
good deal of room for objecting to his reaſoning. After theſe reflections he
is very large in his commendation of the performance of Mr. Clairaut, who
he fays not only calculated ſtrictly the effect of the attraction of jupiter in 1681,
and in 1683 when the comet was again near jupiter, but did not neglect
the attraction of that planet in the years when the comet was moſt diſtant:
that he confidered the uninterrupted attractions of jupiter and faturn upon
the fun and upon the comet; but chiefly the attraction of jupiter upon the
fun, whereby that luminary was a little diſplaced, and gave different ele-
ments
:
562
воок 3
ASTRONOMY
ments to the orbit of the cometa: by this method he found the comet
would be in its perihelion about tht middle of april; but that, upon ac-
count of fome fmall quantities neceffarily neglected in the method of ap-
proximation made ufe of by him, Mr. Clairaut defired to be indulged one
month; and that the comet came juft 30 day days before the time he had
fixed for its appearance.
I would not detract from the merit of the pains taken in going fo mi-
nutely into the affair; but I cannot forbear fetting down a remark made in
a letter now before me of a learned profeffor in Italy to an Engliſh gentle-
man, "Though Mr. De la Lande and fome other French gentlemen have
"taken occafion to find fault with the inaccuracy of Halley's calculation,
"becauſe he himſelf had ſaid he only touched upon it flightly; nevertheleſs
they can never rob him of the honour 1, of finding out that it was one and
"the fame comet which appeared in 1682, 1607, 1531, 1456, 1305:
of having obferved that the planet jupiter would cauſe the inclination
"of the comet to be greater and the period longer: 3, of having foretold
"that the return thereof might be retarded till the end of 1758 or the be-
ginning of 1759 ".
CC
<<
2,
1325 That comets may have their motion diſturbed by the planets, efpe-
cially by the two largeſt jupiter and faturn, appears by an inftance juft now
mentioned: they may alfo affect one another by their mutual gravitation,
when out of the planetary regions; but of this we can take no account, nor
can we eſtimate the refiftance of the ether through which they paſs; and yet
both theſe cauſes may have fome influence upon the fituation of their orbits,
and the length of their periods.
1326 The annual parallax of comets is a proof of the earths revolution
round the fun: it was for want of owning the hypothefis of Copernicus that
Dom. Caffini took what appeared in 1680 and 1681 to be two comets; if
that able aſtronomer had allowed of the annual motion of the earth he could
not have failed to have diſcovered, as Newton did, that it was one and the
fame comet going to its perihelion in the firft of thoſe years and returning
from it in the year following.
1327 Newton obſerved that in the ſolar ſyſtem the ſmalleſt planets are
neareſt to the fun; and thought it probable that in like manner thofe comets
which in their perihelions approach neareſt to the fun are generally the fmall-
eft: this he thought was fo contrived becauſe large bodies in coming fo near
might diſturb the fun. He mentions two purpoſes for which he judged comets
a The effect of jupiters difturbing the fun muft furely be too fmall to make any fuch change in the ele-
ments of a comet as can be diſcovered by obfervation.
t
might
CHAP. 15.
563
ASTRONOMY
might be ferviceable to the folar fyftem; one was, with their atmoſpheres
and tails to fupply the planets with moisture, which is continually wafting
by the growing of vegetables out of water and turning into earth; the other
to recruit the fun with freſh fuel and repair the great confumption of his
light by the streams continually fent forth every way from that luminary :
his opinion was that fuch comes as come very near the fun in their periheli-
ons meet every time with ſo much refiftance from the atmoſphere of the fun as
to abate their projectile force; by the conftant diminution whereof the centri-
petal power or gravitation towards the fun would be fo increafed as to make
them fall therein: in like manner, if we confider the fixt ſtars as fo many funs
furrounded with a number of planets and comets; the appearance of a new
ftar may be owing to one of its comets falling into it, and by the addition
of new fuel cauſing it to blaze out, whereas it had been before for fome time
fo covered over with fpots as to have been invifible.
CHAP. 16. POETICAL RISING AND SETTING OF THE STARS AND
PLANETS: CALENDARS OR ALMANACKS.
F328 The rifing and fetting of the Aars and planets may be confidered in
two refpects; either in relation to the horizon only, or to the fun and the
horizon: the firft, which is uſually meant in common fpeech, is eafily
underſtood; the ftars or planets are properly faid to rife when by the rota-
tion of the earth they appear to come above the horizon; and to ſet when
they appear to go below it: it is obvious that, in this fenfe, to thofe who
live in a right fphere all the ſtars rife and fet every day: to thofe alſo that
live in an oblique fphere all the ſtars which are are not within their arctic
circle, deſcribed § 348, riſe and ſet every day, as was explained more at
large § 355, 356. There are other rifings and fettings of the fixt ſtars by
which the ancient poets, and writers of natural hiſtory or of agriculture
point out the ſeaſons of the year: and theſe relate to the fun as well as to
the horizon.
If a ſtar riſe at the fame time the fun does, the rifing is faid to be cofmicalª;
fo called as if it rofe with the morning of the world: if a ftar fets at fun-
rife, it is faid to fet cofmically.
a From coſmos xooμ the world: this greek word originally fignifies order or beauty; that great
philofopher Pythagoras is faid firſt to have given this name to the beautiful frame of the univerſe.
จ
If
564
BOOK 3.
ASTRONOMY
If a ſtar or planet rife at ſunſet, its rifing is faid to be acrony chala, that
is at the beginning of night; and in this circumſtance the ſtar or planet is
often faid to be acronychal, and ſhines all night: a ftar that fets with the
fun is faid to fet acronychally.
1329 When a ſtar or planet is very near the fun it becomes invifible, by
reaſon of the ſuperior brightneſs of that luminary: the fun does not long con-
tinue to hide the fame ftars; but, by his apparent diurnal progreſs in the
ecliptic, approaches every day nearer to thofe ftars that are eastward from
him; and leaves thofe that are weftward and gets every day farther off
from them.
The light of the fun not only renders thoſe ſtars inviſible that are very
near him, but alſo thoſe that are at a confiderable diſtance from him, and
this diſtance is varied according to the magnitude and brightneſs of the ſtars:
thus, ſtars of the firſt magnitude may be ſeen in ſtronger twilight and nearer
the fun than thoſe of the ſecond: thofe of the fecond nearer than thoſe of
the third, &c. fome of the planets as venus, jupiter and the moon, may be
ſeen nearer to the fun than any of the fixt ſtars can. The ſmalleſt ſtars cannot
be ſeen in the evening before the twilight is quite ended, nor in the morn-
ing after the twilight begins to appear; that is, when the fun is 18° below
the horizon: thoſe of the fixth magnitude require the fun to be depreffed
17° below the horizon; and fo on, they require lefs and leſs depreffion till
we come to ſtars of the first magnitude; which, when on that fide of the
heaven where the fun is, require he fhould be but 12° below the horizon
to render them vifible: mars and faturn muſt have a depreffion of the fun
of 11°, jupiter and mercury of about 10°, venus not above 5°, and ſhe may
often be ſeen in bright funſhine.
I
When the fun is come fo near a ftar as to render it invifible, that ftar is
faid to fet heliacally: when a ſtar that, by reaſon of its nearness to the fun,
has been for ſome time inviſible again comes into view, by the funs getting
to a greater diſtance, it is faid to rife heliacally. Thus we fee fetting heli-
acally is being immerſed in the rays of the fun, and heliacally rifing is
getting clear out of them. It would be a more proper expreffion to call the
firſt of theſe the appearance, the other the occultation of a ſtar.
ap-
The heliacal brifing or fetting is moſt confpicuous in thoſe ſtars that are
near the ecliptic, or not very far diftant from that path wherein the fun
pears to make his annual progreſs: accordingly, ancient writers generally
marked the times of the year by fuch ftars as are within the tropics, or not
very far without them.
Acron nychtos axpov vuxTO is the beginning of the night.
b from helios nλ the fun.
1330
CHAP. 16.
565
ASTRONOMY
1330 The ancient Greek aftronomers in imitation of the Egyptians and
Chaldeans publiſhed calendars or diaries, wherein they noted the rifing and
fetting of fome of the principal ftars; by which they generally meant the
heliacal rifing or the emerfion of the ftars out of the rays of the fun, ſo that
they first appeared in the eaſt before ſunriſe; or the heliacal fetting, that is
their being overtaken by the fun fo as to become inviſible by his being ſo near:
this they did in order to direct their countrymen to the proper ſeaſons for
plowing, fowing and other parts of huſbandry, and to point out to the ma-
riner the ſafeſt times for failing: they gave alfo prognoftics of the wind and
weather, not, fays one of them a, that they thought the changes upon earth
were produced by the ſtars; but, having by long obfervation found what
weather moſt commonly happened at the ſeaſons of the year diſtinguiſhed by
the rifing and ſetting of fuch and ſuch ſtars, they foretold what weather
was like to be in future years, at the rifing and ſetting of the ſame ſtars.
There is one of theſe calendars under the name of Ptolemy, publiſhed by
Petavius; which, if it were not the work of the author whofe name it
bears, feems to have been made in Egypt, by the beginning of the year be-
ing in ſeptember: the following fpecimen will ſhew the nature of it.
Month thoth, or ſeptember.
1. Hour 14, the ſtar in the tail of the lion appears: according to Hipparchus
the etefan winds ceaſe: according to Eudoxus rain and thunder.
2. Hour 14, the lions tail and ſpica virginis are hid: according to Hipparchus
it prognofticates b.
3. Hour 13, the lions tail appears: capella riſes in the evening: according to
the Egyptians the etefian winds ceaſe: according to Eudoxus wind, rain,
thunder: according to Hipparchus the east wind blows.
4. Hour 15, the laft ftar in eridanus fets in the morning: according to
Calippus it prognoſticates, and the etefian winds ceaſe.
5. Hour 13, fpica is hid: hour 15, the bright ſtar in lyra fets in the
morning: according to Metrodorus ftormy: according to Conon the
etefian winds ceafe. &c.
1331 It appears by this fpecimen that the aftronomers therein mentioned
had publiſhed calendars: they lived in different places, and, as each of them
made his calendar for the place wherein he lived, they gave different times
for the rifing and ſetting of the ſame ſtars: for example, lions heart would not
a Geminus, chap. 14. b I fuppofe the meaning is it prognofticates a change of weather, without
faying what the change will be, c Ihave tranflated the greek words as they ftand without knowing what
is meant by the hour: Petavius owns he could not form a conjecture about it: it cannot be the hour of the
day; for many of the appearances paos do not anfwer: nor can the time of them be aſcertained to an
hour: perhaps the original ought to be wpas hours, and then the meaning may be that in places where the
longeft day is fo many hours as the numbers 13, 14, 15, expreſs, the appearances are fuch as are here
deſcribed.
4 C
rife
566
BOOK 3
ASTRONOMY
rife or fet on the fame day and hour at Alexandria in Egypt as at Athens or
Rhodes; by reaſon of the difference in the horizons of thoſe places. The ac-
counts of different authors of the rifing and fetting of the fame ftar in the fame
place would alſo diſagree, if thoſe authors lived in different ages: thus, fpica
virginis rofe in the time of Eudoxus on a different day and hour from its rif-
ing 1000 or 1500 years after, and that becauſe of the preceffion of the equi-
nox, a thing not known till it was difcovered by Hipparchus.
1332 The Romans copied after the Greeks, and indeed made ufe of their
calendars, even after they were known to want correction, as appears by the
confeffion of one of their writers of agriculture a, who ſays that in ſettling
the equinoxes and folftices, he followed Eudoxus and Meton, becauſe the
country people had been long accuſtomed to their accounts, though he knew
of the correction thereof made by Hipparchus.
1333 How the ancient Greeks came to put prognoftics of the weather into.
their calendars has been partly fhewn from one of their beſt aſtronomical wri-
ters, § 1330; that from long obfervation of paſt years they conjectured what
kind of weather would happen at fuch and ſuch times of the years to come.
The obſervations whereon theſe prognoſtics were founded muſt have been of a
number of years, I think it very probable that they took the number con-
tained in the Metonic period of 19 years; for, as within that time the moon
returns to the fame aſpects with the fun, and that planet was thought to have
great influence upon the weather, they might imagin that an.almanack of 19
years would be a perpetual one; not only to mark the days of their ficrifices
and other folemnities, but would ferve alfo to foretell the weather.
1334 That the ancients thought the feveral afpects of the moon had an
influence upon the weather may be feen in Aratus b; where we have rules
for judging what weather is like to happen from the colour of the moon, the
ſhape and fituation of her horns, and other circumſtances of that leffer light.
The Egyptians and Chaldeans, from whom the Greeks had their aftro-
nomy, pretended to foretell the weather, and indeed many other events alfo,
from the aſpects or configurations of the planets: whereof ſome they looked
upon to be hot and dry; others cold or moift: fome benevolent and fortu-
nate in certain fituations; others malevolent and unfortunate.
1335 The ſtars eſpecially thoſe of the brighteſt appearance were thought
to be of the ſame nature with thoſe planets to which they had the neareſt
reſemblance in colour. We cannot wonder at fuch abfurd fancies prevailing
among the ignorant heathen, who held the fun and moon to be their great
gods, and the planets and ſome of the ſtars to be deities of an inferior order,
b in his Διοσημεια or prognofics.
a Columella de re ruftica, 1. 9. c. 14.
or
CHAP. 16.
567
ASTRONOMY
or at leaſt to be the places of their refidence; and therefore paid them di-
vine honours: but that Chriftians who, befides having the light of the
fcriptures, live in an age wherein ſuch improvements in natural philofophy
have been made, ſhould pay any regard to the groundleſs pretences of aſtro-
logers, would be incredible, if we had not examples thereof: it is a mor-
tifying fpeculation to find that no opinion can be broached fo abfurd and
contrary to reafon but that fome partifans will be found ready to ſtand up
in its vindication.
1336 The moon indeed is near enough to be the cauſe of confiderable effects
upon our globe, and all bodies thereon; the raiſes the tides in the ocean, and
cauſes changes in the air, and in the animal and vegetable kingdom: but the
planets even the neareſt of them are at fo great a diſtance from us, that there
is no good reaſon to imagin they have any influence upon our earth or atmo-
fphere; and if they had, how could men ever come to the knowledge thereof?
how could they diſcover that in fome configurations they ſhed a benign in-
fluence, in other fituations had quite contrary effects? as for the fixt ſtars,
their diſtance from us is fo immenſely great, that it is utterly incredible they
ſhould in different pofitions have different effects upon fublunary things.
Sound philoſophy teaches us that the ftars are corporeal, and that bodies at
a diſtance from other bodies can no otherwiſe act upon them than by im-
pulſe or gravitation.
1337 The force of the impulſe of the ſtars we can eſtimate only by the light
they ſend us, and how ſmall this force is we may judge from this, that the light
ſent by all the ſtars in the brighteſt night is leſs than what the moon alone often
gives: as for their attraction or gravitation, that, we know, is reciprocally as
the ſquares of the diſtances of the attracting body: how ſmall then muſt the at-
tracting power be of the neareſt ſtar, the diſtance whereof is ſo immeaſura-
bly great, as we have ſeen, § 888, 889? indeed if the attraction of the ſtars
were more confiderable than it is, they are in fo great a number ſcattered every
way round us that they would balance each other, fo that no particular effect
could follow from any ſmall collection of them. I will not enter into a farther
difcuffion of the credibility of aftrological predictions of the weather; I ſhould
not have ſaid ſo much of it at prefent, if ſpeaking of the ancient calendars
did not put me in mind of the wretched ſtuff our almanacks are filled with
every year; not only about the weather, which their authors would foretell
with as much certainty as they now do, if they were to put the words thun-
der, heat, fhowers, &c. for the fummer months; and the words cold, froſt
and fnow for the winter months, into a bag and ſhake them out at random:
but what is ſtill beyond meaſure ridiculous, they have a column for the parts
4 C 2
of
568
BOOK 3.
ASTRONOMY
of the human body, head, face, neck, throat, breaſt, and fo on down to the feet
and toes, to fhew, and pleafe you, for every day of the year, over what mem-
ber or part of mans body the moon exerciſes dominion: and farther to illuf-
trate this wife conceit, we have the picture of a man ftruck through with
lines, to fhew over what part the fign or conftellation of aries has dominion,
what part is under taurus, gemini, &c: by which they would infinuate, if
any one would regard fuch whimfies, that if you wanted a cure for the
headach, you ſhould make use of the medicine for it at the time when
the moon is in aries; and fo of the reft. Why can they not copy after
the French? they give a great many uſeful things in their almanacks, omit-
ting all predictions of weather or other events; and have in fome of them
given this very good reafon for it, that the Academy of fciences did not think
them to have any foundation in nature.
1338 Sirius is in appearance the largeſt of any of the fixt ftars, is in the
mouth of the conftellation of the great dog, and is commonly called the
dog-ftar: when this ſtar rifes coſmically, as it did anciently in Egypt about
the time of the funs coming to the fummer tropic, the Nile began to riſe,
the overflowing whereof was the great cauſe of the fertility of that country:
this induced the Egyptians to pay divine honours to the dog-ſtar; and to call
a period at the end whereof that ſtar roſe coſmically again on the fame day
of their wandring year, the great year: this period contained 1460 of their
common years 2.
a
They imagined the dog-ftar not only to point out the time of the Niles be-
ginning to rife, but to be the efficient cauſe of its overflowing, or of the fer-
tility confequent thereupon: from the colour of the ſtar at its first appearance,
they formed prognoſtics what kind of ſeaſons they were to expect: if it were
of a golden colour, they thought it prefageda fruitful year; if dim and pale,
they looked upon it as a bad omen that portended a ſcarcity: it may be
doubted whether there were any truth in theſe obſervations or not: if there
were, it muſt be owing to this, that the different colour of the ſtar was cauſed
by the different conftitution of the air; and from that poffibly fome conjec-
tures might be made of the following feafon. They fancied alfo that the
dog-ftar, rifing with the fun and joyning his influence to the fire of that lu-
minary, was the cauſe of the extraordinary heat which uſually falls out in
that ſeaſon: and accordingly they gave the name of the dog-days to about
fix or eight weeks of the hotteft part of fummer.
1339 The Greeks, in imitation of the Egyptians, their maſters in idolatry.
and ſuperſtition as well as ſcience, held the fame opinion of the dog-ſtar being
a v. Cenforin. c. 18. et in cum notas Lindenbrogii.
the
CHAP. 16.
569
ASTRONOMY
the cauſe of that fultry heat ſo often pernicious to the health and life of man :
Homer, comparing the fhining of the armour of Achilles, whofe fury was fo
fatal to the Trojans, to the pernicious blaze of the dog-ſtar rifing at the
end of fummer calls it an ill omen,
"Portending heat intenſe to wretched mortals ".
or as the ſenſe of the paffage is well expreffed by Pope a
— "his burning breath
“Taints the red air with fevers, plagues and death”.
When the father of the poets had faid thus much, it is no wonder the
reft of them ſhould talk of the rage of the dog-ſtar, as fome of them do
alſo of the fury of the lyon b; becauſe a ſtar of the firſt magnitude called
lyons heart, rifing in the time of the dog-days, was alſo thought to contri-
bute towards the great heat of that feafon.
1340 Hippocrates has a ſentence or aphorifm that ſeems to forbid the uſe of
purging medicines in the dog-days; we muſt not conclude from hence that
great phyfician and philofopher to have thought the influence of the dog-ſtar
any thing confiderable; (I have before § 1330, mentioned another learned
Greek who was wiſer than to go into that fooliſh opinion of the vulgar.) It
is probable he only meant to point out the hot time of the year commonly
marked by the rifing of the dog-ftar. Our annual prognofticators, who call
themſelves ftudents in phyfic and aſtrology, would bring us back to the old
Egyptian ſuperſtition, would have us confider the fituation of the ſtars and
planets in taking phyfic, and indeed in all our affairs, as the Mahometans
do at this time.
As to the dog-days by fome attended to with fo much fuperftitious re-
gard, it is pleaſant to ſee what variety of opinions there are both among
the ancients and moderns about the beginning and the end of them: this
variety is in fome inftances owing to the ignorance of the writers, who did
not know the dog-ſtar would rife with the fun on different days in diffe-
rent horizons: ſo that, upon this account, the dog-days would not, in the
fame age begin on the fame day in Egypt as at Athens or Rome: in other
inftances, it is occafioned by the preceffion of the equinox not being known,
or not attended to; and by the imperfection of the Julian year caufing the
ſeaſons to advance, as is fhewn § 1245; by reafon whereof, the dog-ſtar did
not riſe cofmically on the fame day at Rome, for example, in the time of
a illiad, book 22. v. 42.
• Υπο κυνα και προ κινα εργωδίες αι φαρμακείαι.
b Horat. 1.
3.
od. 9.
"jam procyon furit
"Et ftella vefani leonis"
Pliny
570
·BOOK 3
ASTRONOMY
Pliny as it did four or five hundred years before or after: enough may be
feen in Ricciolus upon this fubject, from whom I fhall take two or three
examples in the time of Hippocrates, which he makes to be about 400 years
before the Chriſtian æra, the dog-ftar rofe cofmically in the parallel of Rhodes,
where the pole was elevated 36°, on the 11 of july: at the fettling of the year
by Julius Cæfar, it rofe at Rome on the 18 of july: in the year 1600, it
roſe at Bologna on the 27 of july.
In looking over an ancient calendar in Bede, I find the beginning of the
dog-days placed on the 14 of july: in one prefixed to the common prayer
printed in the time of Q. Elizabeth, the dog-days are faid to begin on the 6
of july, and end on the 5 of ſeptember; and this was continued till the
reſtoration; when that book was revifed, and the dog-days omitted: from
that time to the correction of the British calendar, our alınanacks had the
beginning of the dog-days on the 19 of july, the end on the 28 of auguſt:
fince the correction, the beginning is put on the 30 of july, the end on
the 7 of feptember.
CHAP. 17. THE USE OF THE CELESTIAL GLOBE.
1341 The furniture of this globe is the fame as that of the terreſtrial;
an horizon, a meridian, an hour circle with an index, and a quadrant of
altitude.
ones,
7
Many of the circles which are fometimes imagined to be deſcribed upon
the ſphere of the fixt ſtars are actually drawn upon the celestial globe; as the
celeſtial equator, with fome of its parallels: among theſe the four principal
the tropics and polar circles are drawn with double lines: there are alfo
drawn thereon ſome ſecondaries of the equator or circles of declination; among
them the principal are the two colures: the ecliptic alſo with ſome of its ſe-
condaries or circles of latitude; theſe interſect each other in the poles of the
ecliptic: if there be 6 of theſe circles, their 12 femicircles are drawn through
the points where each of the 12 figns of the zodiac begins, and fhew to which
fign any ftar belongs: thus, all the ſtars comprehended between the femicircle
drawn through the 30 degree of H and the femicircle drawn through the
30 degree of y are in the fign y.
1342 A general idea of the celeſtial globe and its uſe has been given in the
ſecond chapter of the ſecond book from § 603 to the end: if we would uſe
it for any particular purpoſe, the firſt ſtep to be taken is to rectify the globe
to the place, and to the time of the day or night: the rectifying it to the
place
CHAP. 17:
571
ASTRONOMY
place is the fame as that of the terreſtrial globe, ſhewn § 508 & 509: this
done, to ſet it to the time, we muſt firſt rectify it to the noon of the day
propoſed, in the manner following; find the funs place in the ecliptic that
day at noon, by an almanack, or by the calendar ufually pafted upon the
horizon of the globe, and bring that point of the ecliptic to the meridian,
the globe will then exhibit the fituation of the ſtarry heaven as it is at the
noon required; fet the hour index therefore at 12: for any other hour of that
night or day, turn the globe towards the eaſt fide of the horizon if the hour
propoſed be before noon of the day, towards the weſt if the hour be after
noon, till the index points at the hour required; the globe then will ſhew
the fituation of the heaven in the place and at the time in queſtion: thus,
if I would know the fituation of the heaven in London at 10 at night, june
the 1, 1764, rectify the globe to noon at the place and time, and turn the
globe towards the weſt till the index points at 10.
1343 To find the time of the rifing and ſetting of the fun in a given place
on any day of the year, rectify the globe to the place and to the noon of the
day in queſtion, by § 1342, ſet the index at 12, turn the globe eaſtward till the
funs place in the ecliptic comes to the eaſt fide of the horizon, the index will
point at the hour of funrife; turn the globe weftward till the funs place
comes to the weſt ſide of the horizon, the index will then point at the
hour of funſet.
The length of any day in the year at a given place is found by the foregoing
problem, reckoning the time between funrife and funfet.
noon.
1344 To find the declination of the fun at noon for any day of the year:
bring the funs place in the ecliptic to the meridian, and the point of the
graduated edge over it will fhew the declination of the fun that day at
Declination is the neareft diftance from the equator, fee § 783.
1345 To find the right afcenfion of the fun at noon for any day of the year
by the globe: find the funs place in the ecliptic for that day at noon, bring
it to the meridian, obſerve what point of the equator is under the meridian
at the fame time, that degree or part of a degree of the equator is the funs
right aſcenſion for the time in queftion; right afcenfion was explained § 784.
The fun changes his right afcenfion and declination every day of the
year, and indeed continually; not uniformly, but fometimes fafter than at
other times: his declination changes faſteſt at the equinoxes, floweſt near
the folftices.
1346 To find the oblique afcenfion of the fun any day of the year, in a given
latitude, by the globe: rectify the globe to the latitude and to the noon of
the day, by § 1342: bring the funs place in the ecliptic to the eaſt ſide of
the
572
BOOK 3.
ASTRONOMY
the horizon, and obferve what point of the equator in then on the ſame fide
of the horizon, this fhews the oblique afcenfion. While the globe is in this
fituation, the funs amplitude at his rifing on that day, that is his diſtance
from the true eaft point towards either north or fouth, may be feen: by
carrying the funs place to the weft fide of the horizon, his oblique defcenfion
and his amplitude at fetting may be feen. Oblique afcenfion and defcenfion
are explained § 790.
1347 By the fame method as is uſed for the fun the right afcenfion and
declination of a ſtar may be found by the globe.
The converſe of this is true, that if the right afcenfion and declination of
a ſtar be given in a catalogue, or found by obſervation, we may, by bringing
the degree of right afcenfion to the meridian and noting on that circle the
degree and minute of declination, find under the fame the place of the ftar
upon the globe, and, if it be not there already, infert it thereon.
By the preceffion of the equinoctial points, the right afcenfion and decli-
nation of all the ftars are continually changing, the change is confiderable in
a number of ages; but in a ſmall number of years it is hardly perceptible:
in ſome almanacks we have the right aſcenſion and declination of the moſt
remarkable ſtars fet down for the current year: this is uſeful in navigation,
and to find the time of the night at land.
348 To mark the place of a planet upon the globe at any time: many al-
manacks have tables of the places of the planets, from whence they may be
inferted upon the globe, by putting thereon their characters in water colours
without gum; and by rectifying the globe, by § 1342, we may by the
hour index fee the hour of their rifing, fouthing and fetting. The water co-
lours are eafily wiped off with a fpunge or fine rag a little moiftened, if the
globe be varniſhed, as globes generally are. In like manner the rifing, fouth-
ing and fetting of the fixt ftars may be found.
The place of a comet in the heaven may be found by holding the edge of a
ruler fo that the comet may appear between two ſtars and in the fame line
with them, and then holding the ruler fo as to take the comet between two
other ſtars in a right line cutting the former line as nearly at right angles as
can be done with ſtars pretty eaſy to be known: the place of the comet thus
obſerved, may be put upon the globe, by ſtretching two threads in the fame
manner through thofe ftars; the point where thoſe threads interfect one ano-
ther upon the globe is the obſerved place of the comet.
1349 To find the azimuth of the fun at any hour by the globe: azimuths or
vertical circles have already been defcribed § 282: there are none of them
drawn upon the globe, becauſe they vary as the horizon changes; but, when
the
CHAP. 17.
573
ASTRONOMY
the globe is rectified to the horizon of any place, as many azimuths as we
pleaſe may be expreffed by fcrewing the quadrant of altitude to the braſs me-
ridian at the zenith, and turning it round between the horizon and the globe:
the azimuth of the fun at any time is found by rectifying the globe to the
place and time, and carrying the quadrant of altitude round till the graduated
edge thereof paffes through the funs place in the ecliptic; it then ſhews the
azimuth of the fun, which is eſtimated by its diſtance eaſt or weft from the
meridian. The altitude of the fun is ſeen at the fame time, by the number of
degrees upon the edge of the quadrant of altitude between the funs place and
the horizon. The azimuth which cuts the meridian at right angles and paſſes
through the eaſt and weſt points of the horizon is called the primary vertical.
1350 As the ecliptic is drawn upon the terreſtrial globe, all the problems
here mentioned which relate to the fun may be folved by that globe alſo
when a celeſtial one is not at hand: but the proper uſe of that circle
upon
the terreſtrial globe is to fhew over what parts of the earth the fun is vertical
at ncon, and on what days that happens. On the day when the fun is in one
of the tropics he is vertical at noon to every place upon the earth under that
tropic: to every place fituate between the tropics the fun is vertical twice in
a year, once as he goes on declining from the equator to the neareſt tropic:
and again in his return from that tropic towards the equator: in order to
know on what days the fun is vertical to any place, find the latitude of the
place, fuppofe it 12 degrees. north latitude, the fun is vertical at noon
when his declination is 12 degrees north, the fame as the latitude. The ſuns
declination for every day in the year is ſet down in ſome almanacks.
1351 The azimuth and altitude of any ſtar at any time is fhewn upon
the globe rectified to the place and time, by carrying the quadrant of altitude
ſcrewed to the zenith till the graduated edge paffes through the ſtar.
1352 To find by the globe when a ftar rifes cofmically: bring the ſtar to
the eaſt fide of the horizon, obferve what point of the ecliptic is then on the
eaſt fide of the horizon; when the fun appears in that point, (the day whereof
may be known by a calendar) the fun and ſtar riſe together.
To find when a star fets cofmically: bring the ftar to the weft fide of the
horizon, obſerve what point of the ecliptic is then on the eaſt ſide; on the
day the fun appears in that point, the ftar will fet at ſunriſe.
1353 To find by the globe when a ſtar rifes achronycally: bring the ftar to
the eaſt fide of the horizon, obferve what point of the ecliptic is then on
the weft fide of the horizon; on the day the fun appears in that point, the
ſtar riſes at ſunſet. A planet is faid to be achronycal when it is in oppofition
to the fun, and fhines all night.
4 D
To
574
BOOK 3
ASTRONOMY
To find when a ftar fets achronycally: bring the ftar to the weft fide of the
horizon, obferve what point of the ecliptic is then on the weſt fide of the
horizon; on the day when the funs place is in that point of the ecliptic,
the ftar fets when the fun does.
1354 To find when a ftar rifes heliacally: in order to folve this problem
by the globe, the brightneſs and magnitude of the ftar muſt be confidered;
fee § 1329: fuppofe the ftar to be of the firft order, bring it to the eaſt ſide of
the horizon, obſerve by the quadrant of altitude what point of the ecliptic is
then 12 degrees above the weft fide of the horizon, the oppofite point to this
is 12 degrees below the eaſt fide of the horizon, and is the funs place when
the ftar riſes heliacally: on what day the funs place is in the laſt mentioned
point of the ecliptic may be ſeen in a calendar.
To find by the globe when a ftar fets heliacally, fuppofe it to be of the fecond
magnitude, fuch a ftar cannot be feen when the fun is not more than 13 de-
grees below the horizon, § 1329: bring the ftar to the weft fide of the hori-
zon, find by the quadrant of altitude what point of the ecliptic is then 13
degrees above the eaſt fide of the horizon, the point of the ecliptic oppofite
to this is 13 degrees below the horizon; find by a calendar on what day the
point of the ecliptic laſt mentioned is the funs place, that is the day whereon
the ſtar fets heliacally.
1355 To find by the globe the beginning and end of twilight on any day of
the year: the globe being rectified to the latitude of the place, bring the funs
place on the day in queftion to the meridian, ſet the hour index at 12, turn the
globe towards the eaſt till the point of the ecliptic oppofitę to the funs place
is 18 degrees above the weft fide of the horizon, the funs place is then 18
degrees below the eaſt fide, and the morning twilight begins, § 758, the index
will point at the hour. By a like method the time of the ending of the even-
ing twilight is found, by turning the globe till the point of the ecliptic op-
pofite to the funs place on the day in queſtion be 18 degrees above the eaſt
fide of the horizon; the funs place will then be 18 degrees below the weſt
fide of the horizon, when the evening twilight ends; the hour index will
fhew the time.
CHAP.
CHAP. 18.
575
ASTRONOMY
CHAP. 18. THE TRANSIT OF VENUS OVER THE SUN JUNE 6, 1761:
THE PARALLAX OF THE SUN: THE ATMOSPHERE AND SATELLIT
OF VENUS: THE LATITUDE OF CAMBRIDGE FOUND BY A GNOMON.
1356 The publication of my ſecond volume has been retarded by various
unforeſeen accidents, whereof it would be of no ſervice to the public to be
informed: inſtead therefore of apologies for fo long a delay, I thought the
beſt recompence I could make would be to give my readers an account of
ſuch curious obfervations and diſcoveries in aftronomy as have been made
fince I began the work: fome of theſe are very confiderable; as 1, the aber-
ration of light, diſcovered by the late Dr. Bradley, mentioned § 838, &c.
2, the meaſuring the length of a degree upon the earth by fome perfons fent
from France as near to the equator, and others as near to the pole as could
conveniently be done, whereby the figure of the earth is found to be that
of an oblate ſpheroid, flatted at the poles, this Sir Ifaac Newton had before
demonſtrated it to be a priori; as may be ſeen in the 10th chapter of this
3d book: 3, and not to mention any more, the tranfit of venus over the
diſk of the fun, on the 6 of june in the year 1761, whereof ſome account
ſhall now be given.
1357 This curious and uncommon appearance had been predicted by
Halley, and recommended to the attention of aſtronomers, as the moſt likely
means to find out the diſtance of the fun from the earth, § 821. No pheno-
menon in the heaven was ever expected with more impatience, or obſerved
with greater care: for, befides what was done by curious perfons refiding in
different parts of Europe, ſeveral mathematicians furniſhed with proper in-
ſtruments were fent from the R. Society in England, and the R. Academy in
France, to diſtant parts of the earth, to places where it was moſt proper to
make obſervations, and where without this provifion no fuch obfervations
would have been made: a detail of them may be ſeen in the philofophical
tranſactions and the memoires of the French Academy for 1761.
1358 It has before been mentioned, § 313, that if any inſtantaneous pheno-
menon be obſerved at the fame time at two diſtant places of the earth the dif-
ference in hours minutes and feconds, will fhew the different longitudes of
thoſe places, in degrées minutes and feconds: in confequence of this propo-
fition, the difference in hours minutes and feconds in the times when fuch
a phenomenon is ſeen in two diſtant places compared with the difference in
longitude of thoſe places fhews the parallax thereof, provided the latitudes
of thoſe places be alſo known.
4 D 2
1359
576
BOOK 3.
ASTRONOMY
4
1359 As to the preſent affair, the inftantaneous appearances propofed to be
obſerved were 1, the external contact, when the weſtern limb or edge of the
diſk of venus appeared to touch the diſk of the fun, immediately before its
entrance thereon: 2, the internal contact, when the entire difk of venus being
upon the fun the eastern edges of both difks coincided: 3, when the cen-
ters of the fun and the planet were at the leaft diftance from each other:
4, the internal contact of the weſtern edges of the two difks, the moment
before any part of the diſk of venus began to go off from the fun: 5, the
external contact of the edges of the two disks immediately after the total
egrefs of the diſk of venus from off the fun.
1360 The hiſtorian of the R. Academy of ſciences for the year 1761, gives
us, for the refult of the obfervations made by the French, the parallax
of the fun 9": this, fays he, makes the diſtance of the fun from our earth
about a tenth part greater than it was before thought to be; 33 millions of
leagues, whereas it was before computed about 30 millions ª.
1361 Mr. Short, taking the medium of a great number of obfervations of the
tranfit of venus over the fun, calculates the parallax of the fun at his mean
diſtance to be about 8",65: this fets the fun at a ſtill greater diſtance b.
1362 The proportion of the diſtances of the reft of the planets to the diſtance
of the earth from the fun was known before, by their periodical times, for the
fquares of their times are as the cubes of their diſtances: fo that the diſtances
of all the planets from the fun muſt be increaſed in the fame proportion as
the diſtance of the earth is found greater than before it was fuppofed to be.
The ancients made the parallax of the fun a great deal too large; and
confequently held the funs diſtance from the earth to be much leſs than it is.
I have before obferved that Ptolemy and Tycho made the parallax of the
fun 3, Kepler 1, § 815: the laſt mentioned author, who comes the neareſt
to the truth, makes the folar fyftem, though much larger than thoſe before
him, ſtill far inferior to what later and better obſervations have demonſtrated
it to be before the tranfit of venus, the beſt aftonomers had fettled the funs
parallax at no more than 10", a fixth part only of what Kepler held it to be:
by all the accounts of the tranfit of venus, there is more reaſon to think the
funs parallax is leſs, than that it exceeds the quantity laſt mentioned. Thus
we ſee in this inftance, as in many others, that the deeper refearches are
made into the works of creation, and the more perfect knowledge of the
nature of them we are able to attain, the greater and more wonderful do
they always appear.
1363 The learned Dr, Stewart profeffor of mathematics in the Univerſity
of Edinburgh, being of opinion that the diſtance of the fun from the earth
a Hift. de l'Acad. R. 1761. p. 116. ed. Par. b Phil. tranf. 1762. p. 621.
cannot
CHAP. 18.
577
ASTRONOMY
cannot be determined with exactneſs by any obſervations, propofed to folve
this difficult problem by the theory of gravity: this he thought might be done
if the force wherewith the fun affects the gravity of the moon towards the
earth could be aſcertained, as it might be from the motion of the moons
apogee, or from the motion of her nodes. In purſuance of this idea, he has by
a laborious and intricate calculation brought the mean diſtance of the ſun
from the earth to contain 29874,9 mean femidiameters of the earth; which
is more than 118 millions of Engliſh miles, and above a third part greater
than the diſtance computed from taking the parallax of the fun 10": $719.
But is there not as much uncertainty in fome of his data as is likely to
ariſe from the errors of ſo many obſervations? can the motion of the moons
apogee, which we know librates backward and forward, be aſcertained with
a precifion fufficient to build ſo nice a theory upon?
1364 One advantage gained by the obſervations of the tranfit of venus
was fettling the longitude of places where it was obferved, by the times of
the inftantaneous appearances above mentioned. In the tables page 85, the
longitude of Cambridge is ſo faulty that I cannot imagin how thoſe numbers
came there: by the tranfit the longitude of Cambridge in meaſure, is 3 mi-
nutes 45 feconds; in time, 15 feconds eaft of the R. obfervatory at Green-
wich: the latitude of Cambridge there fet down is from Street.
1365 Though the finding the diſtance of the earth from the fun was the
principal object, it was not the only one had in view by thofe who obſerved
the paffage of venus over the fun: it was expected fome other particulars
relating to that planet might on this occafion be known to a greater certainty ;
as the apparent diameter, and the places of the nodes; whether it had an
atmoſphere, and whether it were attended with a fatellit or not.
The apparent diameter of venus upon the fun taking the medium of all
the obſervations was about 57″; this probably is rather fmaller than the
truth; becauſe the fun being fo near venus enlightens more than half her
globe, and confequently the dark part feen by us was not quite half of it:
befides this, the atmoſphere of our earth is faid to have in ſome meaſure the
effect of a prifma; fo that the blue rays from the fun make the upper edge
of his diſk appear higher, the red rays make the under edge appear lower,
by means of this refraction, the perpendicular diameter of the fun is length-
ened about 2": the fame cauſe affected the perpendicular diameter of venus
when upon the fun, but in a contrary manner, for it fhortened it; and this
effect was more fenfible, the greater the refraction; and accordingly Mr.
Chappeb who went to Tobolſk in Siberia to obſerve, found the perpendicular
b ibid. pag. 368.
a. Mem. d'Acad. 1761, pag. 105, & 333. cd. Par.
+
diameter
578
BOOK 3
ASTRONOMY
diameter of venus fhorter in the morning when the fun and the planet were
low, than afterwards when they were got to a greater altitude.
1366 An atmoſphere round venus was thought to be diſcovered by Mr. Hirft
at Fort St. Georgea; for, looking attentively before the ingrefs at the part of
the edge of the funs diſk where he expected the planet would enter, he
plainly perceived a faint penumbra or dufky fhade thereon, and called out to
two gentlemen, who obferved with him, tis a coming; and two or three fe-
conds after happened the firſt external contact, in the moment whereof they
all three agreed: Mr. Hirft could not ſee the penumbra after the egreſs; and
as to the other two perfons one was gone home, the other juſt before un-
luckily loft the planet out of the field of his teleſcope: whatever was the
accident that prevented Mr. Hirft ſeeing the penumbra a ſecond time, Mr.
Dunn bat Chelſea ſaw a penumbra or ſmall diminution of light that grew darker
and darker, for about 5 feconds before the internal contact preceding the
egrefs; from whence he ſeems with good reaſon to determin for an atmo-
ſphere, the height whereof he computes at about 50 geographical miles.
"His obſervations were made with an excellent 6 feet Newtonian reflector,
"with a magnifying power of 110, and alſo of 220 times: he had a clear
dark glaſs near his eye, the funs limb appeared well defined, but a very
"narrow wateriſh penumbra appeared round venus, by which its limb was
"not perfectly defined: at the diſtance of about a fixth part of venus's dia-
"meter from its edge was the darkeſt part of venus's phafis, from which
"to the centre an imperfect light increaſed, and illuminated about the
cc centre." Phil. tranf. 1761. p. 189. May not ſome light from our earth
reach venus when upon or near the fun, as it does the moon in a like fitua-
tion, § 970? if ſo, the middle of the diſk of venus would reflect it towards
us in the greateft quantity; the parts near the edge would fcatter it out of
our view: this depends in fome meaſure upon the nature of the ſurface of
the planet.
Mr. Wargentin who obſerved at Stockholm in Sweden, communicated to a
member of the Royal Society feveral obfervations of the times of the firſt
exterior contact in the more northern parts of Europe; but there is in none
of them any mention of the preceding penumbra ſeen by Mr. Hirst: Mr.
Wargentin fays he could not note the time exactly, becauſe of the undulation
of the limb of the fun; but thought it very remarkable that at the egrefs the
limb of venus that was gone off the fun fhewed itſelf with a faint light du-
ring almoſt the whole time of the emerfion. Mr. Bergman, who was with the
profeffor and others in the obfervatory at Upfal, begins his account d of what
b ibid. 193. c ibid. pag, 213, &c. d ibid. pag. 227.
they
a Phil. tranf. 1761. p. 397.
page 579
Book II
1
132
1
125
128
?
131
126
127
130
129
CHAP. 18.
579
ASTRONOMY
they obferved at the time when venus was entered fo far upon the fun that only FIG.
a fourth part of her diameter was left out of his difk; he fays the part of the
planet that was not come upon the fun was vifible, though dark, and was
furrounded by a crefcent of faint light, as at fig. 125: that this appearance 125
was much more remarkable at the egrefs; for, as foon as any part of the planet
was got off the fun, that part was vifible with a like crefcent but brighter,
fig. 126; and, as venus went farther off, the part of the crefcent that was fartheft 126
from the fun grew fainter, and at length diſappeared, and only the horns could
be feen, as at fig. 127: he fays the total ingrefs was not inftantaneous, but, as 127
two drops of water parting from each other form a ligament between them,
ſo there was a dark fwelling ftretched out from venus to the fun, as fig. 128: 128
and when this ligament broke the limb of venus appeared to be got about
an eighth part of her diameter from the neareſt limb of the fun, fig, 129: 129
he faw the like appearance at the going off, but not fo diſtinct, fig. 130. 130
Mr. Chappe took notice of the part of venus that was not upon the ſun
being visible during part of the time of ingrefs and egrefs; that it was fur-
rounded by a ſmall luminous ring of a deep yellow near the planet that ap-
peared in form of a creſcent; that this was much brighter at the going off
from the fun than at the coming upon him; and that during the time the
whole diſk of venus was upon the fun he faw nothing of it: he fays the
time of the total ingreſs was inftantaneous, like a flaſh of lightening; but
that at the egrefs the limb of the fun began to be obfcured three fcconds
before the interior contact. Some of the French aſtronomers attribute this
faint light round venus to the inflection of the funs rays, as they do alfo
the pale light round the moon in a total eclipſe of the fun: concerning which
fee § 1056. Mr. Chappe makes the principal cauſe of the luminous creſcent
to be the fun enlightening more than half the globe of venus; but in a note
owns this caufe not to be fufficient a
In France, Mr. Fouchy obferved at la Muette, his account is as followeth ;
"during the whole operation we perceived conſtantly round venus a kind
"of ring brighter than the reft of the fun, which grew fainter as it went
"farther from the planet; this crown appeared more vivid the clearer the
“fun was b.” Mr. Ferner profeffor of aftronomy at Upſal obferved at the ſame
place with Mr. Fouchy, and, in a letter to a Fellow of the R. Society has theſe
words; "during the whole time of my obferving with the teleſcope and the
"blue and green glaffes, I perceived a light round about venus, which fol-
"lowed her like a luminous atmoſphere, more or leſs lively according as the
"air was more or lefs clear; its extent altered in the fame manner; nor was,
a Mem: d'Acad. 1761, p. 363. edit. Par. b ibid. p. 100.
<< it
580
BOOK 3.
ASTRONOMY
FIG. "it well terminated, throwing out as it were fome feeble rays on all fides a."
I am not clear as to the meaning of the luminous circle here mentioned,
whether, when the whole planet was upon the fun they faw a ring of light
round it, diftinct from the light of the fun, or whether they mean only the
light that ſurrounded that part of venus that was not upon the fun; Mr. Chappe
takes this and other accounts of the obfervations made in France in this lat-
ter fenfe; and, though he fometimes calls the luminous crefcent that fur-
rounded the part of the planet not upon the fun a ring, he explains himſelf,
that he did ſo becauſe at the coming upon the fun he ſaw it on one fide of
131 the planet, fig. 131, and on the oppoſite fide at the going off, fig. 132; and
132 therefore thought it furrounded it on all fides b.
Upon the whole, the obſervation of Mr. Hirst preceding the firſt exterior
contact, and thoſe of Mr. Dunn and Mr. Chappe preceding the laſt interior
contact are ſtrong indications of an atmoſphere round venus: not to ſay any
thing of the luminous creſcent ſeen upon the parts off the diſk of the fun.
1367 The fatellit of venus was carefully looked for by almoſt all who ob-
ferved on this occafion, but without fuccefs: Mr. Baudouin councellor of the
great council, &c. at Paris, had provided a teleſcope of 25 feet, in order to ob-
ferve the paffage of venus over the fun on the 6 of june, and to look for the fatel-
lit in april and may preceding: he communicated this laſt intention, wherein
he did not fucceed, to a fociety of learned gentlemen at Limoges in the Limofin
in France: Mr. Montaigne one of the members of that fociety was more for-
tunate; for on the 3 of may 1761, at 9h at night, he perceived at 20' diſtance
from venus a ſmall crefcent with the horns pointing the fame way as thoſe
of venus: its diameter was a fourth of that of the primary: a line drawn
from venus to the fatellit made below venus an angle with the vertical of about
20° towards the fouth: though this firſt obſervation was repeated ſeveral
times, Mr. Montaigne was in doubt whether it was not a ſmall ſtar: the next
day may 4, at the fame hour, he ſaw the fame ftar, diftant from venus about
30" or 1' more than before, and making with the vertical an angle of 10°, be-
low but on the north fide; fo that the fatellit ſeemed to have deſcibed an arc
of about 30°, whereof venus was the center, and the radius 20. The two
following nights were hazy, ſo that only venus could be feen: but may 7 at
the fame hour as on the preceding days, he faw the fatellit again, but above
venus, and on the north fide, diftant between 25′ and 26′ upon a line which
made an angle of about 45° with the vertical towards the right hand. The
light of the fatellit was always very weak, but it had always the fame phaſe
with its primary, whether viewed together with it in the field of his teleſcope,
a Phil. tranf. 1761. p. 223.
b Mem. d'Acad. 1761. p. 365.
or
page 581
92
Book II
11
E
Z
134
3
}
B
DC
t
N
133
HOI
CHAP. 18.
581
ASTRONOMY
or alone by it felf: the teleſcope was 9 feet long, and magnified an object FIG.
between 40 and 50 times, had no micrometer, and therefore the diſtances and
magnitudes here mentioned are by eſtimation, wherein he was affifted by
knowing the extent of the field of his teleſcope: confequently great exactneſs
cannot be expected, and therefore Mr. Baudouin ſpeaks with great caution,
and ſays, though the orbit ſeemed to him excentric he would ſuppoſe it to be
circular, not being able to aſcertain the ſmall quantity of its excentricity.
1368 The 133 figure repreſents the three obſervations of Mr. Montaigne, 133
v is the planet venus, z N the vertical, E c a parallel to the ecliptic making
then an angle with the vertical of 45°; the numbers 3, 4, 7, mark the fitu-
ations of the fatellit on the reſpective days. It appears by the figure, that the
points 3 and 7 would have been diametrically oppofite, if the fatellit had
gone 15° more round the point v at the laſt obſervation; ſo that in 4 days
it went through 155°; fay then as 155° to 4 days or 96 hours, fo is 360° to
a fourth number, which gives 9 days 7 hours for the whole fynodical revo-
lution. From theſe obſervations Mr. Baudouin concluded the diſtance of the
fatellit from venus to be about 60 femidiameters of that planet; the orbit
of the fatellit to cut the ecliptic nearly at right angles, to have its afcending
node in 22° of m, and to be in its greateſt northern digreffion on the 7th at
9 at night, and then thought the ſatellit would paſs over the fun with its pri-
mary. Mr. Baudouin, to whom theſe obſervations had been communicated,
read a memoire on the ſubject before the R. Academy of ſciences on the 20
of may, that met with their approbation and was printed.
1369 On the 27 of the fame month Mr. Baudouin read a fecond memoire,
wherein he related another obfervation of the fatellit made by Mr. Montaigne
on the 11 of may at 9 in the evening, the only night when the view thereof
was not obfcured by moonlight, twilight, or clouds: the diſtance of the
fatellit from venus was on the II night much the fame as it had been on
the 7th; that is to fay about 25, making with the vertical at venus an angle
of 45° towards the fouth, and above its primary.
Mr. Baudouin in this laft memoire confirms what he had before fettled
concerning the other elements of the fatellit; but corrects the periodical time,
which, by comparing the firſt obſervation with the laft, he now judged to be
about 12 days; and that, in confequence of this period, the fatellit would not
paſs over the fun, but go at the diſtance of above 20 from his fouthern
limb; though, if the time of its revolution ſhould be 15 hours longer than 12
days, it might then pafs over the fun after venus was gone off.
He thought the reaſon the fatellit had ſo often been looked for without
fuccefs might be, that one part of its globe was cruſted over with ſpots, or
4 E
otherwiſe
582
BOOK 3
ASTRONOMY
FIG. otherwiſe unfit to reflect the light of the fun, as is fuppofed to be the caſe of
the fifth fatellit of faturn, fee § 1201, 1202.
134
Mr. Baudouin obferves that the moſt confiderable confequence that can be
drawn from difcovering a fatellit of venus is the quantity of matter in that
planet: for, by the theory of attraction the maffes of two planets having
fatellits may be found by comparing their diameters, and the diſtances and
periodical times of their fatellits. Newton. princip. l. 3. prop. 8.
By comparing the periodical time of the fatellit and of the moon, he com-
puted the quantity of matter in venus to be near equal to that of our earth:
if this be fo, that planet muſt have confiderable influence upon our earth, in
changing the obliquity of the ecliptic, the latitude and longitude of ſtars, &c.
This with what is faid § 948 and 949, is all we at prefent know of the fa-
tellit of venus, and its elements. In 1769, there will be another tranfit of
venus over the fun, but not viſible in Europe. In the historie and memories
of the R. Academy of ſciences for 1757, there is an account of it, and in
what parts of the earth it may be obſerved.
1370 In the year 1752, affifted by Mr. Dunthorne, I endeavoured to find
the latitude of Cambridge by a gnomon, after the manner deſcribed, § 418
to § 425 on the outſide of the ſouth-eaft corner of the Chapel of Pem-
broke Hall, I fixed a strong round iron bar of about a foot long, fitted
to the bore of a piſtol barrel that it might turn eaſily thereon: to the piſtol
barrel was faſtened a braſs plate about 5 inches fquare, with an hole in the
middle, wherein was put an object glaſs of a 17 feet teleſcope: by means of a
ftring one might ſtand upon the ground and pull the braſs into ſuch a pofi-
tion that the rays of the fun would fall perpendicular upon it, when the glaſs
would give a round image of the fun upon a plane parallel to the braſs: this
image was received upon a marble flab 9 feet long, roughly poliſhed and
placed in my garden upon three ſtrong iron bars each about 4 feet long driven
fo far into the earth that the face of the marble was about a foot above the
furface of the ground: it was exactly levelled with water kept upon it by
being ſurrounded with a low wall of clay; then the water being removed,
a meridian line was drawn thereon, upon which were marked at noon the
extremities of the funs image, now elliptical, for feveral days before and
after the ſummer folftice; the noon of the folftitial day being cloudy.
The length of the perpendicular AB, fig. 134, meaſured from the center
of the glaſs to the marble, was exactly 170.81 inches.
A detail
CHAP. 18.
583
ASTRONOMY
Length-of
Days of
BC in inch.
obfervation and decim.
Angle A C B
altitude of the
funs lower limb
May 31 95-9975 | 60° 41′ 20″
June 1 95.76+ 60 44 57
2 95.5425 60 48 18
61
A detail of the obſervations with the computations therefrom followeth.
Height of the
equator at
Pemb. Hall
37°47′ 32"
37 47 23
I G
Altitude of the funs]
center corrected by
refract. and paral.
Suns declination
from connoiſſance
des Temps.
60° 56′ 44″
44″ | 23° 9′ 12″
61 0 21
23 12 58
3 42
23 16 20
37 47 22
3 95.3775
60 50 50
61
6 14
23 19 19
456 7∞
4 95.21
60 53 25
61 8 49
23 21 49
5 95-0475
60 55 54
61 11 18
23 23 57
37 46 55
37 47
37 47 21
O
6
94.9525
60
57 22
61 12 46
23 25 40
37 47
6
7 94.88
60 58 29
61 13 53
23 26 58
37 46 55
8 94.82
60 59 24
61 14 48
23 27 52
37 46 56
9 94.79
60 59 52
61 15 16
23 28 20
37 46 56
10 cloudy
I
11 94.805
60 59 38
61 15
2
23 28
5
37 46 57
12
94.855
1394.9275
14 cloudy
60 58 52
61 14 16
60
57 45
61 13 9
23 27 18
23 26
37 46 58
7
37 47
2
1595.1575
60 54 13
61 9 37
23 22 34
37 47 3
16 cloudy
17 95.5125 60 48 46
61 4 10
23 17 21
37 46 49
18 cloudy
19 95-9375 60 42 15
60 57 39
23 10 28
37 47 II
20 cloudy
2497.555
60 17 36
60 33 0
22 46 16
37 46 44
Whence the height of the equator
at a medium of the above is
}
เก
The glaſs was not
well centered, ſo that
turning it half round
fhortened B C exactly
two tenths of an inch,
wherefore the above
numbers are to be di-
miniſhed one tenth of
an inch; which was
done before the angles
ACB in the next co-
lumn were computed.
and its complement the latitude
of Pembroke Hall comes out
June the 1, CD was obferved 2.055
9th, it was obſerved 2.05
and 24th, it was obſerved 2.07
37° 47′ 5″
52 12 55
inches
which makes the funs diameter reſpectively
31′ 39″
√31′
31 43″
31′ 36″
To keep off fuperfluous light and make the image of the fun diftinct, a
large ſkreen was placed behind the braſs plate with an hole to let the rays
of the fun through. From a ftiff wire fixed acroſs the center of the glafs
upon
584
BOOK 3
ASTRONOMY
upon a very ſmall wire a leaden weight hung in water to keep it fteady, and
the marble was brought cloſe to it, that the fouth end of the meridian line
might touch the wire when it hung quietly, without preffing it out of the
perpendicular: fome days the wire though always fufpended from the ſame
point would not touch the marble, but there was a fmall ſpace between,
which I took to be owing either to the fwelling of the iron rod by heat, or
the ſhortening of the marble by cold.
On this occafion I meaſured the length of the marble when very much
heated by the fun, driving two nails into a long flip of deal ſo as exactly to
claſp it in length, and then throwing cold water thereon, applied the fame
meaſure to it, and found it was manifeftly fhorter when cold. That metals
expand by heat and ſhrink into lefs dimenfions when cold has long been
known; I do not find any mention made of the like having been expe-
rienced in marble.
BCD.
ERRATA.
Page 292, (in vol. 1.) line 24, for 25% to 91, read 91 to 251. p. 417 (in vol. 2.) 7. 11,
for CHAP. 4 r. CHAP. 5. p. 444 1. 14, and in the margin, for fig. 70 r. 71. ibid. l. 16, for ABC r.
p. 452 in the note, for 1724 r. 1714. p. 453 %. 9, for DCB r. DAB. ibid. l. 10, for B A D r.
BCD. p. 462 l. 11, for 1734 r. 1714. p. 463 1. ult. for 7. Caſſini r. Maraldi. p. 468 1. 4,
for fig. 90 r. 88. p. 469 1. 6, for 1717 r. 1714. p. 470 l. 12, after round, infert fig. 82,
and alfo in the margin. ibid. after are, infert almoft. p. 475 l. 17, for 22 hours and 20
feconds r. 12 hours and 20 minutes. p. 476 1. ult. and in the margin, for fig. 95 r. 96. p. 478 l. 1 & 3,
for 12 r. 25. p. 487 l. 13, for a good way off, r. not far from. ibid. l. 15, for 8° 6′ r. 6° 10′. ibid.
1. 25, after welt, infert, as may be ſeen in fig. 112, 113, and in l. 27, dele the fame words. p. 492 in
the notes, for 588 r. 578. and for as 178 to 179, r. as 229 to 230. p. 497 l. ult. and in the margin, for
fig. 112 r. 115. p. 498 1. 26 and in the margin, for fig. 113 r. 116. p. 499 l. 1 and in the margin, for
fig. 112 r. 115. ibid. 1. 3 and in the margin, for fig. 113 r. 116. 512 7. ult. dele, or of a ſtar.
p.
COGNOSCERE
!
CAVSA
MDCCXXVI
32
NEW
ASTRONOMY, BOOK IV.
CHAP. I. NATURAL PHILOSOPHY WHAT: ITS USE: THE
COSMOGONY OR CREATION OF THE WORLD ACCORDING TO
THE ANCIENT AND MODERN PHILOSOPHERS.
1371 The ſtudy of natural philoſophy is an enquiry into the nature of the
bodies that compofe the univerſe, their caufes, effects, and the manner of
their operations: this ſcience is employed chiefly in confidering the ſyſtem of
the world, the fun, the ftars, planets and comets, with the void ſpace wherein
they are placed: after a general furvey of theſe great objects, it defcends to
a more particular enquiry into the nature of our earth and the ſeveral parts
of it, the air and water that ſurround it; the plants and animals that grow
and live upon it, the metals, minerals and other bodies that are to be found
in the bowels thereof.
In purſuing this ſtudy, befides the fatisfaction that arifes in the human
mind from the diſcovery of truth, it is of great ufe in civil life; for, by
underſtanding the nature of medicines, the phyfician is able to cure diſeaſes,
4 F
and
586
BOOK 4.
ASTRONOMY
and reſtore health, that great bleffing neceffary to make us reliſh all other
enjoyments: and, as to the meaner arts, employed in furniſhing us with the
neceffaries and conveniencies of life, great ufe may be made of the knowledge
of the powers of nature, to affift the labour of man, and enable him to
perform operations far beyond his natural ſtrength, which is the buſineſs
of mechanical ſkill affifted by mathematics.
But the nobleſt fruit to be gathered from fuch fpeculations is this, that
by contemplating the works of creation in a proper way, man is brought to
adore the infinite goodnefs, wiſdom and power manifeftly diſplayed therein;
and at the fame time, while he is ftruck with wonder at the greatneſs and
magnificence of what he underſtands, he is humbled by the confideration
that, after his moft diligent reſearches, much ſtill remains above his compre-
henfion; fo that he muſt at laſt acknowledge that the ways of the almighty
are paft finding out.
1372 Some philofophers both ancient and modern have treated of the
cofmogony, that is, have given us their conjectures how the univerſe was
brought into being: many of the moſt ancient philofophers whofe opinions
have come down to us, though their works are loft, held that the world was
produced out of an indigefted confufed chaos; the matter of this moſt of them,
and Ariftotle amongſt the reft, believed to have exifted from eternity, but
that it was diſpoſed and put into order by an intelligent mind: fome of them
concluded the eternity of the world from a maxim miſunderſtood that
nothing can be produced out of nothing; this is true only in this fenfe, that
nothing can be produced without a caufe, either a material or an efficient
one: as to a material cauſe, in the prefent conftitution of things we do not
indeed find any new productions out of nothing, in as much as all the
changes in natural bodies are made by an alteration in the fituation of their
parts, or by fome of the parts being taken away, or by the addition of other
matter; but this is no objection to the Almighty Creator bringing things
into being which had no exiſtence before.
Another argument for the eternity of the world was taken from the nature
of the Divine Being; who, being always active and benevolent, fome thought,
muſt from eternity have exerted his creative power, that he might have ob-
jects whereon to confer happineſs: to this an anſwer might be given that it
is from no defect of the Divine goodneſs that the world was not made from
eternity, but that there is an impoffibility in the thing itſelf; for whatever
is made by God cannot be coeternal with its maker, but muſt have had a
beginning, and whatever had a beginning there muſt have been a time when
it might be faid it was not a day old. Cudworth, pag. 887.
1373
CHAP. I.
587
ASTRONOMY
4
1373 Befides theſe philofophers, who were all deifts, and acknowledged
one eternal firſt cauſe, incorporeal or diſtinct from matter, which they called
mind, intelligence, the first mover, &c. there were fome few atheistical ones
who pretended to account for all the phenomena of nature by matter and
motion only: of theſe ſome held that matter was endued with active qualities,
that were ſufficient not only to produce plants and brute animals, but men
alfo: others taught that all was the effect of chance; that an infinite num-
ber of extreamly ſmall particles of matter, which, being indivifible, they
called atoms, falling from all eternity at random, through an infinite void
fpace, happened, at a certain time, to juſtle one another, and be entangled;
and cohering together in various manners produced this beautiful frame of
things we now behold. I fhall not attempt a confutation of theſe abfurdities,
it has been done in a maſterly manner by the learned Cudworth in his intel-
lectual fyftem; and fince by others.
1374 Among the modern cofmogonists, Cartes ftands in the first place;
his philoſophy fometime fince made fuch a figure in Europe that it may
not be improper to mention fome of the principles thereof: he recommends
to us in the first place that we ſhould doubt of every thing; in order to get
rid of all kind of prejudices: this doubting being a fpecies of thought, he
concludes the firſt thing a man can be affured of is the exiſtence of himſelf,
that is of his foul that thinks: from the idea we have of a Being of all pof-
fible perfection, he concludes the being of God: from the veracity of the
Deity, who would not deceive us, he argues the reality of the material world :
in his definition of matter, he makes the effence of it to conſiſt in extenfion
only; in confequence whereof, he held the world to be a perfect plenum,
without any vacuity or void ſpace: this he concludes from hence, that we
cannot conceive extenfion without fomething extended; whereas we have as
clear an idea of the extenfion of empty ſpace as we can have of its being
filled: he defines motion to be the carrying a body out of its place among
contiguous bodies that ſurround it into a place where it is furrounded by
other bodies: perhaps this definition, which is true only of relative motion,
was formed to avoid ſome trouble he might have brought upon himſelf by
adopting the Copernican fyftem; for he denied the motion of the earth,
becauſe the atmoſphere furrounding her was carried along with her, in her
revolution round the fun a: he argued from the immutability of the fupreme
Being, that the fame quantity of motion continues in the world as was firſt
impreſt upon matter, confequently that no motion of any body is loft
without being communicated to fome other body.
a part 3. § 19 & 26.
4 F 2
As
588
'BOOK 4:
ASTRONOMY
As to the formation of the Univerſe, he fuppofed it might have been in the
following manner: 1, that matter originally confifted of particles nearly equal
in bulk, of a moderate fize between the greateſt and the leaſt of thoſe whereof
the heaven and heavenly bodies are compofed 2, of irregular figures, not
globular, for then they would not have made a plenum, but there would
have been interftices between them: 2, that each particle was put into a
circular motion round its own center; that thereby the angular or prominent
parts were rubbed off, and each of thoſe alſo by a like circular motion had
their prominent parts rubbed off, and fo on fucceffively, till at laſt that very
fine or fubtile matter was produced, which he called his firſt element: this
he makes a powerful agent, able to penetrate all kinds of bodies: the
particles now made globular he called his fecond element: the third element
was made up of fuch particles as ftill continued angular, uneven and more
grofs.
Beſides this circular motion of fingle particles, he fuppofed collections of
them to have been put into a circular motion round their centers, which
were the ſame with the centers of the fun, ftars, planets and comets, and thus
he accounted for the production of thoſe great bodies. He fuppofes the ſtars
to be made of the first element, the fluid air and ether of the fecond, the
planets and comets of the third. princip. part 3. § 42. He fuppofed that
the fun, in circulating round his own center, cauſes a vortex or whirlpool of
the etherial matter to carry the planets round him the fame way: that the
earth had been originally of the fame nature with the fun; but in time was
cruſted over with ſpots: that, the rapidity of the vortex of the earth being
diminiſhed, the earth with the ambient air was abſorbed into the vortex of
the fun, and carried round him. princip. part 4. § 2. It will not be worth
the while to enter into a farther detail of this philofophical romance, as it has
been juſtly called: enough may be ſeen in Maclaurin's account of Sir Iſaac
Newton's diſcoveries, book 1. chap. 4. In one thing only I think Cartes ought
to have juſtice done him, that he declares he did not think the world was
formed after the manner above deſcribed; but that he apprehended, fuppofing
it had been fo formed, the phenomena of nature would have been fuch as
they now are: he believed that God made the world in a perfect ſtate at once;
in like manner as he created man in his full growth, and not in the ſtate
of infancy. part 3. § 45·
1375 The next attempt to give an account of the formation of the earth
was by Dr. Burnet, a learned man and a fine writer: his defign was to take
a view of our earth through all the great changes it was to undergo, from
a part 3. § 46.
its
CHAP. T.
589
ASTRONOMY
its rife out of a chaos into its paradifiacal ſtate to its being broke into pieces
at the deluge, its deftruction at the general conflagration, its reſtoration to
a fecond paradifiacal ſtate, to be inhabited by the faints for 1000 years, and
after that, its being removed out of its prefent fituation and changed to, what
he conjectured our earth and all the planets originally to have been, a fixt ſtar.
He was particularly concerned to free the Moſaic hiſtory of the deluge from
two great difficulties: one, where to find the great quantity of water neceffary
to drown the earth; the other, how to difpofe of the fame after the flood was
over: in order to this, he fuppofed the earth rofe out of the chaos in the
following manner: 1, that the heaviest parts fell towards the center, and
made there a round folid: 2, that the liquid parts next in weight furrounded
the central folid, and formed the great abyfs: 3, that other fluid particles
lighter than water but heavier than air fell next upon the great abyſs, and
formed thereon an orb oily and unctuous: 4, that the lighteſt particles flew
upwards and conſtituted the air; 5, that the air, not being quite pure, car-
ried along with it ſome grofs and earthy corpufcles, which gradually, as they
could get clear, fell down upon the oily cruſt, and mixing therewith compoſed
the primitive paradifiacal earth, of a ſmooth regular furface, without moun-
tains and without any fea.
He ſuppoſed the diurnal rotation of the earth to have been in the plane
of the ecliptic, fo that there was a perpetual equinox all over the earth:
when he comes to the deluge, he fuppofed the great rains to have been firſt
raiſed up in vapours from the abyss: by the breaking up of the great deep
he underſtood that the exterior cruft of the earth was broke in ſuch a man-
ner as to fall at once in large fragments; that the lower parts of them would
fink down and rest upon the bottom of the abyfs; the upper parts ftanding
irregularly out of the water would conftitute the continents, mountains and
iflands: that the fall of ſuch vaſt maſſes into the abyſs would daſh the waters
thereof above the higheſt mountains: that in this general ruin, by air or
water incloſed between the pieces falling, or by the fragments leaning one
againſt another, many caverns and hollow places now found in the earth,
would be formed. To obviate any miſconſtruction, he declares he would not,
in explaining the deluge by natural cauſes, detract from the power of God, by
which that great judgment was brought upon the world in a providential and
miraculous manner. That the ark ſhould be preſerved ſafe in ſo ſtormy a
ſea, he attributes to a miracle; and accordingly in one of his figures repreſents
it as fupported by two angels. He lays great ftrefs upon the words of St.
Peter, 2d ep. chap. 3. v. 5 &c. which he thought expreffed plainly that the
primitive
590
BOOK 4
ASTRONOMY
primitive earth was prepared for deftruction by a flood, as the poftdiluvian
earth is for being deftroyed by fire.
1376 This theory was attacked by Dr. Keil, Dr. Woodward and others,
and fome part of it was fhewn to be neither agreeable to the Mofaic hiftory,
nor to the principles of found philoſophy: for he afferted the primitive earth
to have had neither fea nor mountains, whereas the Mofaic hiſtory makes
mention of both, Genef. chap. 1. v. 10. and chap. 7. v. 19 & 20.
1377 Dr. Woodward publiſhed an effay towards the natural hiſtory of
the earth; but this is not fo much an account of the formation of the earth,
as an attempt to prove the truth of the univerſal deluge from the pofition of
fhells, teeth and bones of animals found at various depths in the earth; which
he accounts for by a fuppofition, that at the time of the flood the cauſe of the
coheſion of parts in matter was fufpended; fo that every kind of it, earth, clay,
ftones, rocks, metals &c. except fhells and bones a was diffolved into a mish
maſh, or thick fluid; and that, afterwards, every thing fettled according to its
ſpecific gravity, and carried fhells, bones &c. along with it; and that hence
they are found in many places and in great quantities at various depths, not
only in large ftrata or beds depofited upon clay, fand &c. but alſo incorporated
in chalk and marble: he had himſelf obſerved that in England the earth was
diſpoſed in ſtrata, beds or layers, and that ſhells, fishes teeth, and bones were
found in all of them, and this at all depths as far as men had ever digged: and,
by his correfpondence abroad, it appeared the cafe was the fame in all parts
of the earth: but then here is his miſtake; if every thing had fubfided at the
fame time after the flood as he ſuppoſes, the heavieſt bodies muſt have funk
loweſt; whereas we find rocks ftanding upon clay, fand, and earths lighter
than themſelves. It cannot indeed be doubted that chalk, marble &c. wherein
ſhells, teeth &c. are found were in a fluid ftate when fuch bodies were
incloſed in and incorporated with them: it is well known blocks of ſtone
have been formed by the continual acceffion of water, as in Pools hole, and
other fuch places; but the marble that has theſe bodies found in it might have
been confolidated before the flood; and if it were, there is no likelihood it
ſhould then have been diffolved. If it be afked how come fhells to be found
at fo great heights as they fometimes are; we may with Mr. Buffon b allow
that the geography of the earth is at prefent very different from what it
was anciently: the fea has in many parts of the globe encroached upon the
land, and in other parts what is now dry land has been heretofore covered
with the fea: the bottom of the preſent ocean is very uneven, like the land;
a Shells and bones he thought were by their fibrous texture preſerved from diſſolution.
b Hiftoire naturelle.
the
CHAP. I.
591
ASTRONOMY
the flux and reflux affifted by the winds, may often remove whole beds of
ſhells as well as the fands from a deep place to an higher, even to a mountain
in the fea, and there depofit them: and this may have been the cafe both
before and after the flood. As for fhells near the tops of mountains, they
may have been raiſed together with the mountains by Volcanoes.
1378 The famous Leibnitz was of opinion that our earth was originally
a fun, that the greateſt part of the terreſtrial matter was on fire at the time
when Moſes ſays the light was feparated from the darkneſs, that the fire
produced a vitrified cruft, which is the center and foundation of all the matter
contained in the globe: that the fands are fragments of this vitrification; the
other kinds of earth a mixture of fands with falt and water: that when the
central cruft was cooled, the watery particles before raiſed up by the heat fell
down and formed the feas, which at firft covered the whole globe. He
fuppofed alſo the reft of the planets to have been ſtars, which after burning a
long time were extinguiſhed for want of combuſtible matter, and became
opake bodies. Acta eruditor. Lipf. 1693. pag. 40.
· 1379 The next account of the cofmogony was publiſhed by Whiston in
his theory of the earth: he fuppofſes our earth had been originally a comet,
revolving round the fun in an elliptic orbit, which gradually was changed fo
as to come into a circular one, at the time of the Mofaic creation: he fays
the atmoſphere of a comet confifting of various corpufcles in a diforderly
motion anſwers the defcription of that chaos from whence, according to
facred and profane antiquity, our earth took its origin: that the hiftory of
the fix days work is a relation of ſuch appearances and changes as a ſpectator
upon the earth would have obſerved during that time; for example, when
light is faid to have been created on the first day, he imagined that then the
fun, which had long before been created with the ſtars, illuminated the at-
moſphere in ſome meaſure as it does now in a cloudy or miſty day; that on
the fourth day, when the fun, moon and ſtars are ſaid to be made, the
meaning is the air was grown quite clear, fo that they might then all be
feen as to the objection that there was no fuch fpectator upon the earth,
he anſwers that he believed the Meffiah, who created the world and often
appeared in it before his incarnation by the bleffed Virgin, was then upon
the earth, and conducted the formation thereof, kept the journal and com-
municated it to Mofes on the mount a: he ſuppoſes that at firſt the earth had
no rotation round its axis, but revolved round the fun in the plane of the
ecliptic, ſo that the length of the day and night was a whole year: that the
diurnal rotation did not begin till after the fall of our firft parents, and that
a In his answer to Keil.
it
592
BOOK 4
ASTRONOMY
it was cauſed by the impulfe of a comet upon the earth: that the year then
was 360 days, and the month 30: he owns the primitive earth to have had
mountains, but not ſo high as at prefent: that it had ſeas alſo, not ſuch as
they now are, but rather lakes, here and there difperfed; for, if the ocean
had taken up ſo much ſpace as it now does, he thought there would not have
been room enough for the inhabitants, which he apprehended were much
more numerous in the time of the long lived antidiluvians than they have
ever been fince the flood.
He adopts the abyss of Burnet, wherein he fuppofes a magnetic nucleus
to ſwim in order to account for the variation of the needle, concerning which
fee Halley in the Philofophical tranfactions, n. 24. When he comes to the
deluge, he ſuppoſes the great rains of 40 days to have been cauſed by the
earth paffing through the tail of a comet, which he imagins to have been the
famous one that appeared in 1680, with a tail of a prodigious length and
breadth, whereof an account has been given § 1322; and that in this near ap-
proach that comet by its attraction, agitated the abyss, ſo as to make it
burſt the upper cruft of the earth, which is expreſt in ſcripture by the break-
ing up of the great deep. This theory of Whiston was alſo examined by Keil,
but treated with more reſpect than Burnet's had been: he feems well enough
pleaſed with the folution by a comet, but has other objections to which the
author publiſhed an answer,
1380 In the year 1750, Mr. Buffon of the R. Academy of ſciences,
remarked the defects in the feveral theories of the three English authors,
and advanced a theory of his own; which I think for its extravagancy
may vie with any that have yet appeared. He fuppofes that a comet,
coming with great velocity to its perihelion, fell with ſuch a force oblique-
ly upon one fide of the globe of the fun, as to ftrike off therefrom in a
ſtream ſo much matter as the maffes of all the planets amount to: that,
the parts of this ſtream, being of different denfities, were by the force of this
impulſe driven to different diſtances from the fun: fome of the lighteſt were
carried as far as the orbit of faturn, and there by "their mutual attraction
were compacted together, and formed that planet with its ring and fatellits ;
that other parts of a little greater denfity than the former were carried to the
orbit of jupiter, and by mutual attraction compoſed the globe of that planet:
that in like manner the reſt of the planets, mars, the earth, venus and
mercury were formed into their refpective globes, at their proper diftances to
which the matter whereof they confifted had been driven. He mentions
ſeveral arguments which he thinks favourable to his opinion: one is, that
the denſity of the planets is not much different from the denſity of the ſun :
another
CHAP. I.
593
ASTRONOMY
another that the quantity of matter ftruck off from the fun is no more than a
650th part of his whole bulk; for according to Newton the maffes of all the
planets are equal to fuch a part of that luminary: a third argument is, that the
denfity of the planets is greater the nearer they are to the fun; thus, mercury
is more denſe than venus, venus more denfe than the earth, &c. another
argument is, that this fuppofition gives fome account of the cauſe of the
projectile force whereby the planets would be carried on in ſtrait lines, if
they were not retained in their orbits by their gravitation towards the fun;
as it does alſo of the planets all revolving the fame way in their orbits.
He ſuppoſes the diurnal rotation of the earth while it was a burning globe
in fufion would make it become an oblate ſpheroid; that, when it cooled, the
vapours raiſed up by the heat would fall in water upon the furface thereof:
that part of the water mixed with the faline and fulphureous corpufcles going
into the perpendicular fiffures of the earth, produced metals and minerals:
that part of the ſediment of the water formed the original ſurface of the earth,
with which many parts of animal and vegetable ſubſtances are now mixed.
All theſe hypotheſes agree in the notion of a central heat in the earth.
1381 I would not detract from the merit of thoſe learned men, who have
endeavoured to explain the Moſaic hiſtory, and vindicate it from the objections
brought againſt it by the enemies of revealed religion, though they have ſome-
times been miſtaken in the methods of their defence: there are collected in.
Burnet's theory many ancient traditions which confirm the ſcripture account
of the primitive earth, the deluge, &c. In Whifton's theory there are many
philofophical truths laid down, many curious obfervations of the paſt and
preſent ſtate of the earth; but there are alſo ſome fuppofitions not well
enough founded to build fuch a theory upon: when he makes the fix days
creation to be ſo many years, becauſe in ſome of the prophetic writers a day
fignifies a year, this is departing from the text in a plain hiſtorical narration,
which there is no occafion to do, if it be confidered that the almighty power
is able to create the whole univerſe in a moment: again, what he ſays of the
comet coming near the earth at the flood may poffibly be true, but is not fo
eafily demonſtrated to have been the fact as he ſeems to fancy; for, as to his
running the period of 575 years backward and concluding that in its ſeventh
period from the appearance in 1680, it came near our earth; neither is the
time of the revolution of a comet that goes to ſuch a vaſt diſtance from the
fun, where during fo long a courſe it may be diſturbed by other comets,
fufficiently aſcertained, nor is the time of the deluge well enough determined
by chronologers to warrant the conjecture.
4 G
There
594
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ASTRONOMY
There is one error runs through all thefe cofmogonifts, that they ſeem to
have too low and mean notions of the Divine Omnipotence, as if it were
confined to act by human methods: a man going to build a new houſe, will
perhaps, to fave time and expence, pull down fome other buildings, and
make uſe of the materials: but are we therefore to imagin that, when the
Almighty Creator of all things is about to form a planet or an earth, for the
habitation of men and other animals, he muſt caſt about for a fun in decay,
or take a comet out of its orbit whereof to compofe a new world?
Moſes is taken notice of by a celebrated writer of antiquity for the dignity
wherewith he mentions the effect of the Divine power in the production of
light, God faid let there be light, and there was light: may we not fay in like
manner, that God, by the fole effort of his will, brought the fun, ſtars, pla-
nets and comets, the earth and all the plants and animals thereon into being,
in fuch order, and in fuch degree of perfection, as feemed good to his infi-
nite wisdom to beſtow on each of them? The creation of the world was the
miraculous effect of infinite power; and it is a vain prefumption to imagin
we can give a folution of it by mere mechanifm, matter and motion.
1382 Before I mentioned Ariftotle, § 1372, I ſhould have taken notice of
the opinion of his maſter Plato, who plainly afferts that the world was cre-
ated in time; but that the idea thereof fubfifted in the divine mind from all
eternity: that God, induced by his goodneſs, created it when he thought
fit: that when the matter whereof the world confiſts, was before altogether
in a confuſed chaotic ftate, the Divine Being reduced it into order and gave
it a perfect form, which nothing can impair or change but the fame power
that made it: and that it will continue in the fame ftate for ever; becauſe
it is not reaſonable to imagin that a wife and benevolent Being will deſtroy
his own work, which he beheld with pleaſure as foon as he had finiſhed
it. He fays alfo God created the foul of the world before the matter of it:
by the foul he means the nature or the laws of nature. Plato in Timæo.
Thus much may fuffice for an account of the enquiries and conjectures
which have been made concerning the manner how the univerſe was created;
a thing far above human comprehenfion: it is better to confine our felves to
reſearches into the nature and conſtitution of thoſe bodies whereof it confiſts,
and the laws whereby they are governed, in the prefent ftate of things.
CHAP,
CHA P. .2
595
ASTRONOMY
CHAP. 2. THE PRESENT CONSTITUTION OF THE UNI-
VERSE ACCORDING TO THE ANCIENTS AND MODERNS:
THE NEWTONIAN PHILOSOPHY: DEFINITIONS OF TIME,
SPACE, MATTER AND MOTION.
1383 The moſt ancient philofophers among the Greeks, who borrowed
the greateſt part of their learning from the Chaldeans and Egyptians, held,
that all material beings confifted of atoms; fome of them were of opinion
that the atoms were fimilar, others that they were diffimilar: that by
different combinations of theſe atoms the four elements fire, air, earth, and
water were formed: that the difference between the feveral natural bodies
aroſe from the different proportions of theſe elements which entered into
their compofition: thefe atomical philofophers, who all, except a few, Demo-
critus, Leucippus and Epicurus, &c, believed the whole to be directed by a ſu-
preme intelligent Being, are faid to have learned their notions from one Mofchus
a Phenician, whom fome learned men have thought to be the fame with Mofes
the Jewiſh hiſtorian and lawgiver: they all held a vacuum or void ſpace.
Befides theſe, we know but little of their tenets; fome of which are menti-
oned by Ariftotle, who endeavoured to confute them; as alfo by Laertius,
Pliny, in a treatiſe among the works of Plutarch and by Stobaus. Among
the moderns fee Cudworth and Stanley.
1384 Some of the ancient Greeks travelled into Egypt where learning then
flouriſhed: from thence Thales, the founder of the Ionic ſchool, brought his
idea of water being the principle of all things; which feems to be derived
from the tradition of our earth taking its origin from a chaos or fluid maſs
of heterogeneous mixture: fome of his fucceffors taught that the fun and ſtars
were earths heated to a great degree: that the ſtars, like the fun had earths car-
ried round them: that the moon would fall to the earth, if ſhe were not whirled
round as a ſtone in a fling: quotations to this purpoſe may be ſeen in Gregory's
preface to his aſtronomy; that author will have it that they had the know-
ledge of mutual gravitation of matter, and of the laws thereof: if he had
remembered the doctrine of Empedocles about the alternate fucceffion of
friendſhip and averfion to each other, perhaps he might have found therein
the modern diſcoveries of attraction and repulfion: but this fure is being too
partial in favour of the ancients, to imagin they exhauſted the whole trea-
fure of natural knowledge, and left nothing for thoſe that came after them
to diſcover.
In Egypt Pythagoras learned the true fyftem of the
4 G 2
world
596
BOOK 4.
ASTRONOMY
world; which, though he left nothing in writing himſelf, was maintained
by his fcholars.
1385 When Ariftotle came to teach philoſophy at Athens, he contra-
dicted moſt of thoſe who went before him; and, according to the cuſtom
that then prevailed, began a new fect of philofophers, which grew to be
fo much in vogue beyond all the reft, that his opinions were looked upon
as inconteſtable. He taught a plenum, that all is full of matter, and that
there is no fuch thing as void ſpace in nature: in aſtronomy he maintained
that the firſt cauſe which is intelligent, gave motion to the primum mobile,
or outermoft orb of the heavens, whereby the diurnal motion of all the hea-
venly bodies is produced; but that the fun, moon, and planets are carried
round in their ſeveral periods a contrary way, each in its own ſolid orb: that
the heavens and heavenly bodies confift of a celeſtial matter fuperior to that
of the four elements, and are ingenerable and incorruptible, never had a
beginning, and are not liable to any change: that comets are nothing but
meteors or exhalations raiſed out of the earth by the heat of the fun and car-
ried up into the ether above our atmoſphere, where they burn till the matter
of them is confumed: that the cauſe of the levity of flame is that it endea-
vours to riſe up to its proper place the ſphere of fire, which he imagined
to be above the air: and that the gravity or weight of the earth is cauſed
by a tendency towards its own place which is loweſt.
As to all fublunary bodies, he held that the three principles from which
they ſprung, are privation, matter, and form: when privation is made a
principle, it can only mean the ftatus a quo, that every thing becomes what
it is from having been fomething elfe before; for example, a table is made out
of ſomething that was not a table before: this furely improves our knowledge
very little: his materia prima or original matter is to be conceived diveſted
of all properties, quantities and qualities; to be neither folid nor fluid, hard
nor ſoft, &c. ſo that ſome have thought it would be reduced to nothing: form
is that which makes any thing to be what it is, diſtinguiſhed from all other
things: now, becauſe in every animal there is, befides fenfeleſs matter, fome
ſubſtance added thereto that has life, makes it to be an animal, the followers
of Ariftotle will have every inanimate thing to have alſo a ſubſtance annexed
to it, which is the form thereof: thus fubftantial forms were introduced into
the philofophy of the ſchools; whereas in truth what makes the difference
in natural bodies is an affemblage of circumftances or accidents peculiar to
each of them; thus, gold is diſtinguiſhed from all other metals by its weight,
colour, ductility, being indifolvable in aqua fortis, diſolvable in aqua regia.
See Boyle of forms and qualities.
1386
CHAP. 2.
597
ASTRONOMY
1386 The principal advances in natural philoſophy made by the moderns
are, the reviving the old Pythagorean fyftem by Copernicus, and the defence
thereof by Galileo and Kepler: the diſcoveries by Tycho Brahe that co-
mets move at a greater diſtance from our earth than the moon: the laws
of motion in falling bodies found by Galileo: the laws of motion in the pla-
nets by Kepler: the invention of teleſcopes, microſcopes and the air pump
opened a large field of philofophy unknown to the ancients: to which
may be added, great improvements in anatomy and chymistry; and the faci-
litating the communication of this and all other kind of knowledge by
printing. I pafs by the vortexes and fubtle matter of des Cartes as precarious
fuppofitions now generally exploded, and proceed to confider the philofophi-
cal principles of Sir Ifaac Newton.
1387 That great author, as profeffor Cotes obferves in his preface to
the fecond edition of the principia, ufes partly the analytic, partly the
fynthetic method: in the analytic, by a number of experiments and ob-
fervations, he enquires what the laws of nature are; and theſe being found,
in the fynthetic he concludes how they will operate upon various bodies:
thus, having found that gravity is a property which univerfally belongs to
all bodies near our earth, he firft, from the motion of the moon, demon-
ftrated that planet to have the fame gravitation towards the earth as all
other bodies have: in like manner, from the motion of the primary planets
round the fun, he proved their gravitation towards that luminary; and again
from the gravitation of the ſecondary planets, partly towards their primaries
and partly towards the fun, he fhewed what were the laws of their motions,
and particularly with regard to the moon, gave a more correct theory of her
motion than had ever before appeared; and demonſtrated a priori that ſhe
muſt, from that two-fold gravitation, have all thofe inequalities which
aſtronomers have by incredible labour obſerved. That this is the beft
method of philoſophizing is evident from the following rules laid down by
the author in his third book,
1. We ſhould allow of no more caufes of phenomena than are neceffary:
becauſe nature is fimple, frugal, and does nothing in vain.
2. When effects are the fame, we ſhould affign the fame cauſes, if it be
poffible: thus the fall of a ſtone to the earth in Europe is by the fame
cauſe as in America: heat is the fame in the fun as in a common fire:
reflection of light on the earth is the fame as in the planets.
3. Such qualities as are found in all bodies we are acquainted with may
be looked upon as generally belonging to all kind of bodies: fuch as
exten-
598
BOOK 4
ASTRONOMY
extenfion, folidity, impenetrability, mobility, paffiveneſs or inactivity:
to which we may add mutual gravitation.
1388
Time, Space, place, and motion, are words often made uſe of, but
are in philoſophy frequently underſtood in a different ſenſe from the mean-
ing of them in common fpeech; to prevent miſtakes, they may be confidered
abſolutely or relatively. The following definitions are according to the
Newtonian philoſophy.
Abfolute time or fimple duration, confifts of moments following one another
in a continual fucceffion, flowing uniformly without any relation to any cre-
ated being, has been the fame from all eternity, and will for ever continue
the fame. Relative time is fome portion of abfolute time, which our ſenſes
meaſure by the apparent motion of one of the heavenly bodies, or by fome
machine that meaſures that motion; as a clock, a watch, &c. thus we come
by our idea of a year, a month, a day, and the parts thereof, as an hour,
a minute, &c.
Time may be conceived to be divided into parts leſs and lefs without
end: I have ſeen a watch with an hand that in a ſecond of time went round
a circle divided into four equal parts. In aftronomical calculations, not only
feconds, but thirds, fourths, and fifths are fometimes employed: the leaſt
part of time that is fenfible may be different to different perfons; as in ſeeing
fome eyes are able to perceive a ſmaller object than others.
Abſolute ſpace is always the fame, immoveable, capable of receiving all kind
of bodies, extended without limit: we may conceive it divifible into parts
leſs and leſs without end, but they cannot be feparated from one another.
Relative Space is ſome part of abfolute ſpace of certain dimenfions; thus we
may meaſure the infide of an empty caſk, of a room in an houſe; or we
inay even confider the dimenfions of the ſpace wherein the whole folar
fyftem is contained.
Abſolute place of a body is that part of abſolute ſpace occupied or filled
therewith, at any given time. Relative place of a body is its fituation deter-
mined by other bodies that furround it, or are near it: by the rotation of the
earth, London changes its abfolute place continually; but its place in re-
lation to the globe of the earth continues the fame: thus alfo the apparent
or relative place of a planet or comet at any time is confidered among the
fixed ſtars; which, as far as our fenfes inform us, remain invariably in the
fame part of abfolute ſpace.
Abfolute motion of a body, is its being removed out of one part of abſolute
ſpace into another. This motion is fometimes diſcovered by the cauſes thereof,
or the power acting thereon; as impulfe, or attraction: fometimes it is known
by
CHAP. 2:
599
ASTRONOMY
by its effects; thus, one proof of the rotation of our earth round its axis is
taken from the ſhape thereof, being an oblate ſpheroid, rifing higher at the
equator, and the gravity of heavy bodies being there diminiſhed by the cen-
trifugal force; as appears by this, that the pendulum of a clock adjuſted to
other parts of the globe will there go too flow, and muſt be fhortened to
make it keep true time. Relative motion of a body is the change of its relative
place: apparent motion is when by the real motion of the ſpectator one way,
other bodies that are at reft ſeem to move the contrary way: thus, to a man
fitting in a ſhip failing eastward, the ſhores and buildings in view ſeem to
move weftward: thus, by our earth turning round its axis, the heavenly bodies
appear to go round us: thus alſo the earths annual revolution in her orbit
makes the fun appear to go round the ecliptic.
1389 Matter or body is a fubftance extended in length breadth and thick-
nefs, limited by fome figure or ſhape, divifible, impenetrable, and moveable,
conſiſting of parts feparable from one another; the divifibility of matter into
parts leſs and leſs without end, at leaſt in conception, is evident from
hence, that we cannot imagin the ſmalleſt particle thereof to be laid upon
a plane, but we must neceffarily conceive that the lower fide of it touches
the plane, and the upper fide does not: that matter is actually diviſible
into an inconceivable number of parts is evident, from many experiments:
one grain of gold will gild a prodigious number of yards of wire: one
drop of a chymical coloured liquor will vifibly tinge many gallons of water:
one grain of perfume will diffuſe a ſcent through every part of a large room:
fee Boyle of the nature of effluvia. Shaw's abridg., vol. 1. pag. 403. How
fmall the particles of light muſt be was hinted § 228. By the impenetrability
of matter is meant that it ſo fills the place it occupies, that no other
body can enter therein without difplacing the firft; thus, if a wedge be
driven into a piece of wood, it ſeparates the parts of the wood afunder: if a
foft body be compreffed fo as to take up lefs room than it did before, this is
done by forcing fome other matter out of its pores; as when air or water is
fqueezed out of a fpunge; if a peice of metal be hammered fo as to leffen the
pores and bring the parts thereof cloſer together, this will make it leſs in
bulk. By the mobility of matter is meant that it may be carried out of its
place by the impulſe of other matter; thus, a bullet is fent out of a gun
by the force of expanded air: a ball is driven to a diſtance by the ſtroke
of a racquet.
1390 All matter is of itſelf purely paffive, can neither when at reſt put it-
felf in motion, nor when in motion bring itſelf to be at reft, but equally re-
fifts any change of either of theſe ſtates into the other: this is called the
vis
600
BOOK 4
ASTRONOMY
vis inertia or the power of inactivity in matter: from which it comes to paſs
that there is required the fame force to put any mafs of matter into any
given degree of motion, as there is to ftop it, when going on with that
degree of motion. If a body be at reft, it will for ever continue in the
fame place, if not difturbed by any other thing; if a body be in motion,
it will for ever continue to move at the fame rate in a ſtrait line, if not
obſtructed or turned out of the way by fome external force; this is matter
of obſervation and experience. Ariſtotle alſo taught that matter is paffive.
1391 The quantity of matter in any body is estimated by the folid parts,
not by the bulk thereof; becauſe all bodies we are acquainted with contain
pores void of matter; and even in the heaviest bodies yet known, their pores
take up more ſpace than the ſolid parts do. Newt. optics b. 2. prop. 8. The
quantity of matter in any body is known by its weight.
1392 The quantity of motion is meaſured by the quantity of matter and the
velocity of the motion of the body moved taken together, i. e. by multiplying
one by the other: for the motion of the whole body is the ſum of the mo-
tions of all its parts: in two bodies that are equal in quantity of matter, the
motion of each is as its refpective velocity: in two bodies A and в equal in
quantity of matter, if a moves with double the velocity of B, the motion
of A is double, or the force that cauſed it is double to that of B: again, let
A be double to B, to make both move with equal velocity, the force applied
to a muſt be double to the force applied to B; if I would compare the
quantity of motion in two bodies A and B; fuppofe A contains a quantity of
matter expreffed by 4, or weighs 4 pound, and moves with a velocity of 2
miles in a minute, multiply 4 by 2, the product 8 expreffes the quantity of
motion: fuppofe the quantity of matter in в is 6 pound, the velocity of B 3
miles in a minute, let 6 be multiplied by 3, the product is 18. I fay the
quantity of motion in A to that of B, is as 8 to 18.
1393 Impreſſed force is an action exerted upon a body to change the ſtate
thereof with regard to motion or reft: this force is not to be conceived as
motion inherent in the body moved, and pushing it forward; for, if that
were the cafe, fuch continual addition would produce not an uniform, but an
accelerated motion like that of falling bodies: the force confifts in the
fimple action which cauſes the change; and the body continues in the
new ſtate into which the change is made by the vis inertia alone. An
impreffed force may arife from different cauſes; as percuffion, preffure, at-
traction or centripetal force.
Percuffion is the cauſe of motion when one body ftrikes upon another,
thus a ball is put into motion by the ftroke of a racquet. If a veffel full of
water
CHAP. 2.
601
ASTRONOMY
water has an hole made near the bottom, a ſtream will run out of it with
greater or lefs velocity, according as the preſſure or weight of the incumbent
water is greater or lefs: and this weight is eſtimated, not by the largeneſs of
the ſurface, but by the height of the columns of water in the veſſel above
the hole: a clock is kept going by preffure of the weight, or the ſpring.
1394 By centripetal force is meant any force whereby a body is made to tend
towards any point as a center, fuch is gravity, whereby all bodies upon
or near the earth have a tendency towards the center of the earth: fuch
is the power of the loadſtone to attract iron, fuch is the force whereby
the planets are continually kept from flying off in tangents to their orbits
and compelled to revolve round the fun; in like manner as a ſtone in a fling,
when whirled round, continually endeavours to fly off in a tangent to the
circle, but is retained by the hand that holds the ftring. The quantity of
centripetal force may be confidered as abfolute, accelerated, motive.
1395 The abfolute quantity of a centripetal force or attraction is meaſured
by the ſtrength of the cauſe thereof: thus, the magnetic power of one load-
ſtone is greater than that of another.
1396 The quantity of an accelerative centripetal force is meaſured by the
velocity it cauſes in the body moved thereby, in a given time: thus, the force
of the fame loadſtone is greater the nearer the iron is to it: thus, the force of
gravity is greater, and makes a body defcend with greater velocity in a valley
or near the fea; than on the top of an high mountain, fee § 1409.
1397 The motive centripetal force of a body is the weight thereof; and is
measured by the oppofite force which balances the fame: thus, an heavy body
in one ſcale is prevented from defcending towards the center of the earth by
another body of equal weight put into the other ſcale.
1398 Befides thoſe mentioned § 1389, there is another property of mat-
ter that ſeems not to be effential, but to be fuperadded to it by the Almighty
and All-wife Creator, to render it more uſeful for the purpoſes it was made to
ſerve; and that is gravity or mutual attraction, whereby every particle of
matter has a tendency towards every other particle: this attraction is of two
kinds, the attraction of cobefion, whereby fmall bodies placed afunder at very
fmall diſtances approach one another, and unite into one mafs; or whereby
parts
of the fame body adhere and ſtick together: thus, two ſmall drops of
quickfilver placed very near each other, will unite together and run into
one drop: in folid bodies, the hardneſs of fome is thought to be owing to the
parts in contact touching one another in many points: thus we fee in
glafs that is broken, the furfaces parted are ſmooth, ſo as to ſhew they were
in cloſe contact before they were feparated.
4 H
1399
}
602
BOOK 4
ASTRONOMY
1399 The other fort of attraction or gravitation, is that which operates
at a diſtance: of this we fee daily inftances in the falling of heavy bodies to
the earth: this in a falling ftone may be called gravitation, and is the fame
with its weight or tendency towards the center of the earth; in the earth we
call it attraction, as if the power that moves it refided in the earth: the truth
is, the tendency is reciprocal; and if the ftone were equal in quantity of
matter to the earth, thofe bodies would approach towards each other with
equal motions; whereas, the difference between the quantity of matter of a
common ftone and the earth being enormously great, the motion of the ſtone
is
very fenfible; but the tendency of the earth to the ſtone ſo inconceivably
finall, that the earth may be confidered as perfectly at reft; and therefore
we ſay the ſtone gravitates towards the earth, and not the earth towards the
ftone: we fay alſo the earth attracts the ſtone, not that the ſtone attracts
the earth. To diſtinguiſh it from ſome others of a more confined nature, this
attraction may be called general attraction; becauſe it is extended not only to
all bodies upon the earth, but alſo to the fun, planets, and comets. The
great attraction of the earth is the caufe that the mutual attraction of fmaller
bodies is not perceptible.
1400 Of this action of bodies upon each other at a diftance, no mechanical
cauſe can be affigned: as for the opinion that it may be effected by ſome
fubtle ethereal medium; whatever motion fuch a medium may be ſuppoſed
to have, and to communicate to the various bodies in the univerfe, it ſeems
probable it might ſcatter them different ways; but it can never be fhewn that
it would drive them one towards another, except it were directed by ſome
intelligent agent: let half a dozen corks or other light bodies be held down
to the bottom of a tub full of water, if let go, the fluid will force them up-
wards, but not towards each other. We obferve many inſtances of ſagacity in
the brute creation, in providing for fecurity againſt what would injure them
or their offspring; and we ſay they are directed by inſtinct; the meaning
whereof muſt be, that the author of their being, by fome way unknown to
us, difpofes them to fuch actions as tend to their fafety: what reafon have
we then to exclude from any part of the material world the influence of that
Almighty benevolent Being, who is intimately preſent in all the parts of his
own work, and ſupports every thing in fuch order as feems meet to his infi-
nite wiſdom? if it be faid that the buſineſs of philofophers is to point out
mechanical cauſes, this is true ſo far as we are able to diſcover them; and
yet all muſt at laſt be refolved into the will of the Divine architect, who
diſpoſed the ſeveral parts of the creation to act upon one another in the man-
ner they do; and gave them laws, which, fo long as he thinks fit to continue
them,
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603
ASTRONOMY
them, ſhall not be broken: thofe laws are commonly called the laws of nature,
into theſe and the manner of their operation, it is the part of a philofopher
to enquire; and the only method of fearching them out is, by making expe-
riments and obſervations upon the bodies that are within our reach.
Sir Ifaac Newton's laws of motion.
1401 In the Newtonian philoſophy the laws of nature are firſt found by
experiments, and then from thoſe laws the phenomena of nature are de-
duced. The 1 law, every body or parcel of matter would continue in its pre-
ſent ſtate of reſt or motion if not diſturbed by fome external caufe: this is a
confequence of the inactivity or paffive nature of matter, mentioned § 1390,
and is evident from experience; for if a body be laid in any place, there we
are ſure to find it at any time afterwards, if nothing removes it: and, as to
perfiſting in motion, every projectile or body thrown forward with any force,
as a bullet ſhot out of a gun, would for ever perfift to go on in a ſtrait line
with the fame velocity, if it met with no obſtruction; whereof this is a plain
proof that the bullet has no power to make any change in its own motion.
It is true, near the earth, a bullet ſhot out of a gun goes but a very little
way with the greateſt velocity, or in the firſt direction given to it: for there are
two caufes of the change in the motion thereof; 1, the velocity is gradually
retarded by the refiftance of the air, and 2, gravity brings it continually nearer
to the earth, and prevailing over the projectile force, makes it fall down.
1402 The 2d law, all motion, or change in motion is proportional to the force
that is the cauſe thereof: thus, if a given force moves a body with a certain
degree of velocity, double that force will move the fame with a double ve-
locity: a treble force will move it three times as faft, &c. in confequence of
this law, if a body A in motion be impelled by another body в in the fame
direction, a will have its motion accelerated more or lefs in proportion to
the ſtrength of the impulfe. If B impells A in a contrary direction it will
take away ſo much of the motion of A as the motion of B amounts to: if B
impells a with an oblique ſtroke, it will alter the motion of A, and cauſe it
to go on in a direction compounded out of its own original direction and
the direction of B.
1403 What has now been ſaid of impulſe is applicable alſo to attractive
force; a body in motion, if attracted the fame way it is going, will be ac-
celerated; if a contrary way, will be retarded in its motion: if with an oblique
attraction, it will fuffer a change both in its velocity and its direction.
1404 And here, as a corollary or confequence, it may be proper to lay down
the following propofition; if a body be acted upon by two forces, whereof
one may be repreſented by one fide, the other by one end of a parallelogram,
4 H 2
the
604
BOOK 4.
ASTRONOMY
FIG. the motion arifing from thoſe two forces combined will be in a diagonal':
1 thus, fig. 1, if a body be urged by a force fufficient to carry it in a certain time
from A to B, and at the fame moment be acted upon by another force, that
in the fame time would carry it from a toc, it is demonftrable that theſe two
forces combined would cauſe it to go in the diagonal AD. From this pro-
pofition the converſe follows, that any motion in a ſtrait line AD may be
reſolved into two directions, by drawing a parallelogram fo as to make AD
the diagonal thereof.
1405 The 3d law, reaction is always equal and contrary to action; if a
body a acts upon another B with a given force, whether impulfe or attraction,
B acts upon A with an equal force, and in a contrary direction.
Thus, when an hammer ſtrikes upon an anvil, the anvil returns the
ftroke: if a man ftrikes his hand againſt a ſtone the fame effect will follow, as
if the ſtone ſtruck his hand with equal force: if an horſe by a rope pulls againſt
a load, the load pulls the horſe with an equal force: this will be evident if the
rope when upon the ſtretch be cut in the middle; the two halves of it will
then fly with equal velocity, one towards the horſe, the other towards the
load: again, if a man in a boat upon a ſtill water, pulls another boat of equal
bulk and weight, the two boats pull equally; for they will approach each
other with equal velocity, and meet in the middle of the way: if a loadſtone,
be laid upon a little boat of cork in a tub of water, and a ſmall piece of iron
upon another cork be brought within the ſphere of the loadſtones attractive
power, they will both move towards each other, with different velocities,
but with an equal quantity of motion; for the iron will move as much. fafter
than the loadſtone as the loadſtone is heavier than the iron, § 1391.
Action and reaction are ſeen in rowing, fwimming, and flying; when the
oar of a rower puſhes the water one way, the water puſhes the boat the con-
trary way: in ſwimming, a man puſhing the water one way, the water drives
him the contrary way: when a bird beats the air backwards with his wings,
the air drives the bird forwards: when a bird beats the air downwards with a
force exactly equal to his own weight, as an hawk fometimes does, he is
ſuſpended in the air, without making any progreffive motion.
CHAP. 3. GRAVITATION OR ATTRACTION: THE LAWS OF
FALLING BODIES: PENDULUMS: PROJECTILES: CENTRI-
FUGAL FORCE: REPULSION: ELECTRICITY.
1406 That all kind of bodies at the fame diſtance from the earth gravitate
towards the fame, or weigh more or lefs according to the quantity of matter
in them, as was ſaid § 1391, may be illuſtrated by the following fuppofitions ;
I,
CHAP. 3.
605
ASTRONOMY
1, the atoms or ſmalleſt particles whereof bodies are compofed are fimilar;
2, every atom has a like gravitation: now if we imagin every atom of an
heavy body, as for inſtance a ſtone, to have one end of a thread tied thereto,
and the other end to be faftened to an atom in the earth, we may eaſily con-
ceive why the gravity of a body is greater or lefs according to the quan-
tity of matter or the number of atoms whereof it confifts: for a body a
that has one thouſand atoms is attracted as if it were pulled by a thouſand
threads;
another body в with two thouſand atoms is attracted as if pulled
by two thouſand threads; they will therefore both of them move with
equal velocity; becauſe they are each of them urged with a force proporti-
onal to the quantity of matter to be put into motion: the double quantity
is moved with double force: for this reafon a cubic inch of lead weighs more
than a cubic inch of wood; becauſe there are a much greater number of
atoms in the lead than in the wood.
Theſe two bodies weigh unequally in a balance, becauſe the heavier body
having a greater momentum preffes the ſcale with double the force of the
other: they do however when all obftructions are removed, as in the exhauſted
receiver of an air pump, fall to the earth. with equal velocity; becauſe each
body is urged by a force proportional to its quantity of matter; the double
quantity is acted upon by a double force.
1407 If the earth contained more matter than it does, its attraction would
be ſtronger, and all bodies near it would be heavier than they now are: for
we may confider a ſtone of one pound weight as if it were pulled by as many
threads as there are atoms in the earth: ſo that if the earth had twice the
quantity of matter, that is twice the number of atoms, the ſame ſtone would
weigh two pound, as if it were pulled by twice as many threads.
Corollary. The fame body at a given diſtance from the center of jupiter
would weigh as much more than at the like diſtance from the center of the
earth as the quantity of matter in jupiter is greater than in the earth: in the
fame manner the weight of any body upon the fun or any of the planets may
be eſtimated; or converfely, the attraction of a planet being found, the
quantity of matter therein may be known.
1408 The mutual attraction or gravitation of bodies is not a new notion, but
has been mentioned as a probable thing by ſeveral writers: Sir Ifaac Newton
was the firſt who, by a large induction of particulars, proved the truth and
univerfality of it: and, by a fublime geometry fearched out the laws by
which this power acts: he gives us a caution that when he uſes the words
attraction or gravitation he would not be underſtood to affign the mechanical
cauſe of the operations performed thereby: this he owns to be unknown; yet
does
ง
606
BOOK 4
ASTRONOMY
does not bring into philofophy occult qualities in the fenfe of the Ariftotelians,
who pretended thofe qualities arofe from their forms, allowed by them to
be things unknown; and therefore their faying a phenomenon aroſe from fome
occult quality was the fame as if they had ſaid they knew nothing about it:
whereas in the Newtonian philoſophy attraction or gravitation is ſhewn to
be univerfal, reaching, without any exception, through the whole viſible
fyftem; not only to all kind of bodies upon our earth, but even to the fun,
moon, planets and comets. And, although we are ignorant of the cauſe of
this power, it may be of great ufe to determine the laws and inveſtigate the
confequences of it.
1409 The law of this gravitation is, that it decreaſes in the fame pro-
portion as the fquares of the diſtance between the attracting bodies increaſe;
thus, a ſtone near the furface of the earth tends towards the center with a
force four times as great, or weighs four times as heavy, as it would do if
it were twice as far diftant from the center. We cannot indeed carry any
body to fuch an height above the earth as to make experiments of this;
but the pendulum of a clock of the fame length performing its vibrations
quicker when carried near the equator than when near the poles, is a de-
monftration of the truth of what is here afferted, as will be fhewn
hereafter.
1410 At the fame diſtance from the earth, taking away the reſiſtance of
the air, gravity equally accelerates all falling bodies, whether great or ſmall
heavy or light: this appears by an experiment made by an air-pump with
a long receiver exhaufted, in the top whereof was placed a feather, a piece of
paper and a guinea; if theſe be ſo held as to be all let fall at the fame moment,
they will all come to the bottom of the receiver at the fame time. That all
kind of bodies at the fame diſtance from the earth gravitate equally, or are
of equal weight in proportion to the quantity of matter, is farther evident by
the following experiment; let any number of boxes be prepared of the fame
ſhape and fize, that the refiftance of the air may be equal to all of them;
into each put different matter; into one lead, into another iron, into a third
wood, &c. ſo as to make each box with what is contained therein of equal
weight, fuppofe two pound; let them be all ſeverally fufpended with lines
of equal length: if they be all drawn at the ſame time to equal diſtances
from the perpendicular fituation, they will all, like fo many pendulums,
keep exactly the ſame time in their courſes and recourſes.
In the firft of thefe experiments, the refiftance of the air being taken off,
all bodies fall together with the fame velocity: in the ſecond, the boxes being
all equal in ſurface, the reſiſtance of the air is the fame to all of them: and
I
the
CHAP. 3.
607
ASTRONOMY
the boxes being all-equal in weight, they all keep equal time in their fwings. FIG.
1411 Aweight ſuſpended upon a pin by a ftring or wire is called a pendulum:
the length of the pendulum is meaſured from the pin, which is called the
point of fufpenfion, to the center of gravity of the weight: fig. 2, if the 2
weight be drawn to c and let go, the force of gravity would carry it down-
wards in the line CD; but, being confined by the ftring it cannot go out of
the circle, and must therefore go towards E, and will by acceleration in its
fall acquire force enough to carry it up to A, an height equal to that of c
from whence it fell; from a it will then with the fame force as before fall to
E and rife to c, and from thence back again to A, and fo on without ceafing,
if it were not for the refiftance of the air, and the friction of the pin; but
thoſe two caufes will gradually abate the length of its fwings, till at last it
fettles at reft in E. The weight for a clock is uſually of a lenticular form,
that it maypaſs through the air the more eafily.
The ſhorter the length of a pendulum is the quicker are its fwings, and
that in the following proportion; the fquares of the times of the ſwings are
inverſely as the lengths of the pendulums: if the length of a pendulum be one
foot it will ſwing twice as faſt as one of 4 feet.
As theair is fome times more denſe and its refiſtance greater than at other
times, the ſwings of the fame pendulum will not always reach to the ſame
length of ſpace; if the fwings be made in a circle, longer fwings will take
longer times: a fmall fpring is ufually placed at the upper end of the pendu-
lum to a clock, whereby the weight, inſtead of a circle, is made to go nearly
in the arc of a curve called a cycloid: by this means the fwings will be in
equal times, though unequal in length.
A wire or bar of metal is lengthened by heat, and ſhortened by cold, and
brafs more than iron: to remedy this inconvenience in the pendulum of a
clock, Mr. Graham fixed to the rod a weight of quickfilver contained in a
glafs with a tube, wherein the quickfilver ſhould rife by heat, fo as to keep-
the center of gravity of the weight always at the fame diſtance from the point
of ſuſpenſion: others have invented what is called the gridiron pendulum, a com-
bination of braſs and iron wires fo to counteract one another, as to keep the
pendulum of the fame length, in hot or cold weather: others have attempted
the fame thing by the lever pendulum: fome have made uſe of a ſmall rod of
wood painted over, to prevent it from imbibing any moiſture from the air:
this laſt I have been told has fucceeded very well; wood is not apt to fwell.
or fhrink lengthways of the grain.
142 Any heavy body, as a ſtone, a bullet of lead, &c. let fall from a.
confiderable height may eafily be obferved to defcend with greater velocity
the
608
BOOK 4
ASTRONOMY
FIG. the nearer it comes to the ground: the law of this acceleration, firſt diſco-
vered by Galileo, is this, the ſpace a falling body goes through (ſetting afide
the refiftance of the air) is as the fquares of the times, reckoned from the
beginning of its fall: for inftance, let the whole time the body is falling be
divided into any number of very ſmall parts, which to avoid a multiplicity
of words may be called moments, whatever be the length of the line gone
through in the firſt moment, in 2 fuch moments it will go though 4 of thoſe
lengths; in 3 fuch moments it will go through 9 of thofe lengths; in 4 it
will go though 16 of thoſe lengths, &c.
I
1413 It appears from experiments made by feveral perfons that an heavy
body near the earth (abſtracting from the refiftance of the air) falls 16
Engliſh feet and 1 inch in a fecond of time: when I fay near the earth, I
mean if let fall from the higheſt place we can go to, as the top of an high
tower, or of a mountain; for all fuch heights bear fo fmall a proportion to
the femidiameter of the earth as to be quite inconfiderable. See in Defaguliers
experimental philofophy, vol. 1. p. 342. an account of letting fall leaden
bullets from the top of the infide of the cupola of St. Pauls London.
The diſtance of the furface of the earth from the center at the equator is
feveral miles greater than at the poles, § 1191; perhaps the difference in
falling bodies near the equator or near one of the poles would fcarcely be
perceptible; but a pendulum by a number of ofcillations will diſcover it:
and accordingly, a clock that went very well at Paris required to have the
pendulum ſhortened to bring it to true time when carried near the equator.
1414 When a body near the earth is projected or thrown in any other di-
rection befides that towards the center it is called a projectile: and is faid to
be driven by a projectile force: an arrow ſent from a bow, or a ball ſhot out
of a gun is a projectile.
14:15 If a body be thrown upwards in a line perpendicular to the horizon,
3 fig. 3, it will in its afcent, by its gravity towards the earth, be continually
retarded, ſo as to rife flower and flower, till it is got to the utmoſt height
to which the impelling force can carry it; from thence it defcends with
an accelerated motion in the manner deſcribed § 1412.
3
At all points of equal diftance from the earth as B, C, D, the fame body
goes with equal velocity defcending as it did afcending: for it is equally af-
fected by gravity at each of thoſe points, both in the aſcent and deſcent.
1416 Aball ſhot out of a gun if it met with no obſtruction would, by the firſt
law of motion, go on for ever in a ſtrait line with the fame velocity; whereas
it goes ſo but a little way, becauſe it is retarded by the refiftance of the air, and
is by gravity pulled continually nearer to the earth, and made to deſcribe a
curve
CHAP. 3.
609
ASTRONOMY
curve called a parabola, § 191, the line wherein it moves bending more and FIG.
more downwards till it falls upon the earth, fig. 4.
The greater the force of the powder is the farther will the ball
go before it
falls to the earth: we may fuppofe a ball to be thrown with force enough
to carry it 20, 40, or even 100 miles, though no engin can be invented of force
fufficient for that effect; and if it could be thrown even 1000 miles, the
centripetal force being ſtronger than the projectile would bring it gradually
nearer the earth, and at laſt cauſe it to fall thereon.
We may farther
ſuppoſe a ball to be thrown horizontally, at a ſmall diſtance from the earth,
with a velocity that would carry it the length of a great circle upon the earth,
in a given time, and we may ſuppoſe it to be acted upon by a centripetal force
adequate to the projectile; i. e. juft fufficient to balance the fame, neither
too weak ſo as to permit the ball to be carried farther from the earth, nor
too ſtrong ſo as to bring it nearer; in this cafe, it would, if the refiftance of
the air were taken away, continue for ever to circulate round the earth, at a
ſmall diſtance from the furface thereof: for, by the first law of motion, it
would continue to go forward with the fame velocity, and the centripetal
force would continually bend its direction towards the earth, and prevent
its receding farther from it, in the fame manner as a ſtone whirled in a
fling is hindred from flying off, ſo long as the hand holds the ſtring.
1417 If a body be projected in the line A B, fig. 5, and attracted at the
fame time towards fome point out of the line of its direction as s, it will
deſcribe a curve whofe concave fide fhall be towards the centripetal point;
for the line it goes in will fall continually below AB, the line of its firſt
direction: and a line drawn from that point to the body will ſweep over
equal areas in equal times, whether the center be at reſt, or moves uni-
formly in a ſtrait line.
4
1418 If a body, by adequate projectile and centripetal forces, be carried with
an uniform velocity in a circle, a line drawn from the center to the circum-
ference of the circle will fweep over equal areas in equal times; that is to ſay,
the triangular areas ASB, BSC, CSD, &c. fig. 6, will be equal: this is
obvious in a circle; becauſe the arcs AB, BC, CD, &c. gone through in
equal times being equal, and the fides AS, BS, CS, DS, &c. being likewife
equal, the triangles are equal.
1419 This propofition is alſo true with regard to any body carried round the
focus of an ellipfis, and urged with a centripetal force adequate to the projec-
tile towards the focus, that a line drawn from the focus to the body moving
in the circumference of the ellipfis will pafs over equal areas in equal times
as before. See the following figure.
5
6
Let
610
BOOK 4.
ASTRONOMY
FIG.
Let the time be divided into equal parts, in the firſt part of time let the body,
7 by whatever impulfe, go from A to B, fig. 7, in the fecond part, if nothing
hindred, it would, by the first law of motion, go on an equal length from
B to c, then the line BS would fweep over a triangle B sc equal to ASB: but
when the body is at B, let the centripetal force act upon it, fo as in the fame
time that its impulfe would carry it to c, the centripetal force would car-
ry it to v; compleat the parallelogram BVCC, and the body will go to c
in the diagonal BC, by § 1404. Now cc being parallel to SB, the triangles
SBC and SBC will be equal, becauſe they are between parallel lines SB
and cc: by the fame argument, will each triangle SCD, SDE, SEF &C.
be proved equal to SBA. If any number of thoſe triangles be added together,
the total fums as ADS and FCs will be proportional to the times wherein
they are deſcribed.
If the lines AB, BC &c. be continued round a center, they will form a polygon;
and if the fides of the polygon be indefinitely increaſed in number, and
indefinitely decreafed in length, they will form a curve, a circle, or an
ellipfis: and the propofition will be true of thoſe curves, that a line drawn
from the center to a body in the circumference of the circle, or from the focus
to a body in the circumference of the ellipfis, will fweep equal areas in equal
times. Newton. princip. p. 35 edit. Cantab. 1713.
1420 The converfe of the propofition immediately preceding is alſo
true, that where the line drawn from the central point to a body going in the
circumference of a circle, or from the focus to a body going in the circum-
ference of an ellipfis, ſweeps equal areas in equal times, the body revolving
round in a circle or ellipfis is urged by a contripetal force towards the center
of the circle, or the focus of the ellipfis. Newt. ibid.
From hence it is proved, that the planets and comets are all urged with
a centripetal force towards the fun; becaufe lines drawn from every one of them
to the fun, fweep over equal areas in equal times: by the fame argument,
it is alſo proved, that every fecondary planet is urged with a centripetal force
towards its primary: thus, the moon defcribes equal areas in equal times
round the earth; as does alfo every fatellit of jupiter round jupiter; every
fatellit of faturn round faturn: this is true, except when the centripetal force
is diſturbed by the gravitation of fome other body: the moons motion is
diſturbed, that is, fometimes retarded, fometimes accelerated by the fun, as
will be fhewn hereafter.
1421 The fame propofition will help us to illuftrate and explain the re-
volutions of the primary planets, in elliptical orbits, not much differing
from circles, round the fun, in one of the focufes of each ellipfis.
One
CHAP. 3.
611
ASTRONOMY
One example will ſerve to illuftrate what has been faid: let the ellipfis FIG.
A B C D E F G H I K LM, fig. 8, reprefent the orbit of a planet, going therein ac- 8
cording to the order of the letters, round the fun at s, in one of the focufes
of the ellipfis; and let the time of its revolution be divided into any number
of equal parts, fuppofe twelve: in coming from a through B, C, D, &c. the
planet approaches nearer to the fun; and, the centripetal force continually
increafing its velocity, goes through greater arcs in equal times, till it comes
to G; from thence its motion continually carries it to a greater diftance
from the fun, and confequently its velocity is retarded by the attraction of
the fun, and it defcribes in equal times, arcs. lefs and lefs, till it returns to A;
from whence it proceeds as before: now the triangular areas paffed over by
the line drawn from the planet to the center of the fun, in equal times, will
be equal; becauſe, as in the planets going in the first half of the ellipfis, from
A to G, the arcs, which may be confidered as the bafes of the mixed triangles,
deſcribed in equal times grow longer and longer, the legs grow fhorter, fo
as to keep the triangular areas equal: in the other half of the ellipfis, in the
planets going from its perihelion at G to its aphelion at A, the arcs grow
horter, but their ſhortneſs is compenfated by the greater length of the legs,
ſo as to make the areas of the ſeveral triangles exactly equal.
1422 If a body thrown by a projectile force in a direction AE, is at the
fame time urged by an adequate centripetal force, in a direction perpendicular
to the line of the projectile force, it will defcribe a circle; and, if it meet
with no refiftance, will go perpetually round in the fame. See fig. 6.
If the line wherein a body is carried by a projectile force makes an ob-
lique angle with the line of the direction of the centripetal force, and the
two forces be adequate one to the other, the body will be carried round
in an ellipfis, whereof the central or attracting point fhall be one of the
focuſes. See fig. 9 and 10.
6
9
If the line of projection AB fig. 9, makes an acute angle BAF, with the
line of direction of the centripetal force AF, the body will approach
nearer to the attracting point, how fmall foever the force be wherewith it is
attracted. If the line of projection AB fig. 10, makes an obtufe angle BAG, 10
with the line of direction of the centripetal force AG, the body will recede
farther off from the attracting point, how great foever the attracting force be.
1423 Let us now confider the projectile and centripetal forces together,
as they are compounded in the revolutions of the primary planets round the fun:
If the projectile force or velocity of a planet be adequate to the centripetal,
that is, if they be fo: adjusted that neither can overcome the other, and at
the beginning of the revolution, the direction of the projectile force were in
4 I 2
a
612
BOOK 4.
ASTRONOMY
FIG. a tangent to a circle perpendicular to the radius, or line of direction of the
centripetal force, the planet would be carried round in a circle, and meeting
with no refiftance, continue to go in the fame for ever; for, by the laws of
nature, the planet by reafon of its inactivity, being once put into motion the
velocity muſt continue the fame, and the centripetal force continuing the
fame alſo, perpetually bends it down to the fame diſtance from the ſun.
9
If the projectile and centripetal forces being adequate as above mentioned,
the line of the projectile force makes an oblique angle with the line of di-
rection of the centripetal force, the planet muft revolve in an ellipfis,
whereof the fun would be in one focus, fig. 9 and 10.
1424 If at the beginning of the planets revolution, the centripetal force
acting at right angles to the projectile be too ftrong for the fame, the planet
will deſcribe an ellipfis, fig. 9, and the point a from whence the planet ſet
out will be its aphelion: but, if the centripetal force be too weak for the
projectile, it will go in an ellipfis having its perihelion in the point where
10 it began its motion, fig. 10.
1425 When a planet is carried in an ellipfis round the fun at s, according
11 to the order of the letters fig. 11, as it goes from A to B, from в through
CDP, it approaches nearer to the fun, making an acute angle with the line
drawn to the focus; its velocity thereby increaſes all the way to the perihelion;
there the directions of the two forces are at right angles with each other;
but the projectile force is ſo increaſed as to overcome the centripetal, and
confequently carry it farther from the fun; in its progreſs though the other
half of the ellipfis PQRTA; there gradually receding from the fun, and
making an obtuſe angle with a line drawn to the focus; it is therefore
retarded by the funs attraction, all the way to the aphelion at A, and in
going to that diſtance from the fun, the projectile force is fo weakened that
the centripetal force prevails over it, and brings it down again through
ABCD &c. and thus it goes on for ever, the centripetal force and projectile
prevailing alternately.
1426 When a planet moves in an ellipfis round the fun, the line of di-
rection of the projectile motion is every where inclined in an oblique angle with
the direction of the centripetal, except in two points, the aphelion and pe-
rihelion. In the aphelion, a planet is fo fituated that the line of direction
of the projectile force is perpendicular to the direction of the centripetal; it
will not however go on in a circle, becauſe there the centripetal force prevails,
and brings it down towards the fun: in the perihelion alſo, thoſe two
lines of direction are one perpendicular to the other; but there the projec-
tile force is too ftrong for the centripetal, and therefore carries the planet
farther off from the fun..
1427

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Book IV.
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a
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94
m
B
n
17.
18
A
30
AIND
CHAP. 3.
613
ASTRONOMY
1427 Whiston was of opinion, that all the planets originally revolved round FIG.
the fun in cirles, and all in the fame plane; and that the cauſe of their mo-
tions being now in ellipfes and in different planes was the near approach of
comets: for a comet coming near a planet on the eaſt fide would, by attract-
ing it the fame way it was a going, accelerate its motion, and make it go in an
ellipfis, larger than its original circle: but a comet approaching near a planet
on the weft fide would retard its motion, and cauſe it to go in an ellipfis lets
than the circle wherein it before revolved; and that, if a comet moving in a
different plane came near a planet, it would attract it in ſuch a manner as to
make it revolve in a new plane nearer to the plane of the comet.
1428 Every body whirled round in a circle endeavours continually, during
its revolution, to fly off in a tangent to the circle it deſcribes; this appears
by various experiments: let a ſtone in a fling be carried round in the circle
A B C D according to the order of the letters, fig. 12. when the ſtone is at a, 12
if it be let looſe, it will fly off in the tangent Aa: if it be let looſe when at
B, it will fly off in Bb: if let looſe at c, it will fly off in cc, &c. the force
which urges the ſtone is called a centrifugal force; becauſe it tends to
carry it farther and farther from the center of the circle; though not
in a direct line from the center. The like effect of the centrifugal force may
be ſeen in the drops of water thrown from the rim of a mill-wheel im-
merſed in water and going ſwiftly round: as alſo, to mention a more homely
experiment, in the drops that fly from a wet mop whirled briſkly round.
1429 The greater the velocity is wherewith a body is carried round, the
ftronger is the centrifugal force: thus, the quicker a ſtone is whirled round
in a fling, the farther will it go when let loofe. While the ſtone is retained
in its circular motion, the centrifugal and the centripetal forces may be faid to
be equal; the ſtring is pulled equally by the ſtone and by the hand which holds
it, § 1405. If a ſtone in a fling be whirled round with fuch velocity that the
centrifugal force is greater than the ſtrength of the ſtring can counterbalance,,
the ſtring will be broken and the ſtone fly off.
As a planet is whirled round the fun, the projectile force may be con-
fidered as centrifugal, in as much as it would fly off in a tangent, if the
centripetal force were to ceaſe acting thereon.
1430 In a globe which has a rotation round its axis,. the ſeveral parts of
the furface thereof are carried with different degrees of velocity,, and confe-
quently with different degrees of centrifugal motion; in the parts near the
poles this motion is very flow; in the equatoreal parts it is quickeſt: and.
this is the cauſe of the earth being a flatted ſpheroid. See § 1199.
143 F
614
BOOK 4*
ASTRONOMY
RIG
13
1431 The moon is impelled round her orbit by a projectile farce, and retained
from flying off in a tangent, by a centripetal force adeqate to the projectile,
that is, by her gravitation towards the earth: that the centripetal force urges
the moon towards the earth is evident by § 1420.
That the gravitation of the moon towards the earth is of the fame nature
with that which makes heavy bodies fall to the earth, mentioned § 1398, 1399,
and follows the fame rule, given § 1409, was firſt diſcovered by Sir Ifaac
Newton, and is proved in the following manner: the time of one revolution
of the moon round the earth, is known to be 27d 7h 43′ 5″: from thence
may be computed what arc fhe goes in her orbit in one minute of time:
let it be the arc AB, fig. 13, draw AD which will fhew how far the moon
would be carried by the projectile force alone in one minute, draw BC parallel
to AD, AC will be equal to DB, and fhews how far the moon would fall to-
wards the earth by the centripetal force alone in one minute; A C is equal to the
verfed fine of the arc A B: this is found to be 3600 times leſs than the ſpace a
falling body near the earth is carried through in a minute: now the diſtance of
the moon being 60 femidiameters of the earth, her gravitation is 60 multiplied
by 60 or 3600 times lefs than the gravitation of bodies near the earth; and
confequently the gravitation of the moon follows the fame rule as that of other
bodies mentioned § 1409. See the calculation in Whiston's prelect. math.
1432 When jupiter and faturn are near conjunction, they diſturb each others
motions; as hath been obferved by aftronomers: near the fame conjunctions
alſo, ſome irregularities have been obſerved in the fatellits of jupiter, which
they are not ſubject to at other times, and are owing, no doubt, to the
attraction of ſo large a body as that of faturn. Comets may be diſturbed by
fome of the larger planets, and by one another: that this might not often
happen, is probably the reafon why their orbits are not fo nearly in the fame
planes as thoſe of the planets, but are variouſly placed, that they might
not come near one another in their aphelions, where their projectile and
centripetal forces are weakeſt, and where they might moft eafily be dif
turbed. See § 1324 & 1325.
1433 The general mutual gravitation or attraction of matter is proved by
various experimets: it is by gravitation that the particles of light are bent,
in paffing very near to any ſolid body, § 220. That the rays of light are
refracted in paffing out of one medium into another of a different denſity,
213: it is by attraction that ſeveral operations in chemiſtry are performed,
as diffolutions, precipitations, &c. of which fee Boyle's works epitomized by
Shaw, vol. 1. in the article precipitation. Newtons optics, pag. 355. &c.
Friends prelectiones chemica: to the fame cauſe is owing the afcent of liquors
in
CHAP. 3!
615
ASTRONOMY
in capillary tubes: and partly the rifing of the fap in trees and plants: it is
the fame power that raiſes the tides; namely, the gravity of the water to-
wards the fun and moon, eſpecially the moon, which, though greatly infe-
rior to the fun in bulk, on account of her being vaftly nearer to the earth, has a
much ſtronger effect, as will appear when we come to confider the tides:
the fame attraction of the moon is the cauſe of the preceffion of the equinox;
wherein the attraction of venus and jupiter are alſo thought to have fome
Thare, of which more hereafter. Thus is the truth of the fact eſtabliſhed with
regard to mutual gravitation of all kind of bodies, whether in the heaven
or on the earth.
1434 Befides the general mutual gravitation or attraction of matter, which
operates according to the fame law as is obferved in all forces or powers that
are diffufed from a center, as light, heat, &c. § 88 & 1409. There are alſo
particular attractions obfervable in fome forts of bodies, as amber, fealing wax,
glafs, and fome precious ftones, which, warmed a little by rubbing, have a
power of attracting light bodies, as little bits of paper, feathers, filk, thread, &c.
thefe bodies are faid to be electrical, from electrum, the latin word for amber,
in which, this property was firſt or principally obſerved.
The loadſtone has a particular attraction which it exerts only towards iron,
when near it, and is faid to be diminiſhed in a ratio of a cube and a quarter of
its diſtance: that is, if the diftance be twice as great, the attraction will
Defaguliers courfe of experimental philoſophy vol. 1.
be 10 times as weak.
p. 16 & 40. but fee § 1438. Befides theſe, there are particular attractions be-
tween certain bodies, as between fulphureous bodies and light; for light acts
with greater force upon fuch bodies than upon any other, and will fooner
kindle them into fire and flame. Newt. optics, quere 7. Salt of tartar attracts
the watery particles that float in the air, which other falts will not do, ibid P.
351. Water and oil of vitriol poured fucceffively into the fame veffel grow hot
in mixing, which heat argues a great motion in the liquors, and this motion
is a proof that the liquors rufh towards one another. That the fame acid
liquor is attracted by one metal more than another is evident from experi-
ments, for aqua fortis will diffolve filver and not gold; aqua regia will
diffolve gold and not filver. Newton's optics p. 357.
1435 There is another property of matter, in fome bodies at leaſt, contrary
to attraction, and that is repulfion: we have feveral inftances of this which
ſhall now be mentioned; in electrical experiments, the fame body which in
ſome circumſtances is attracted, in others will be repelled: a glafs tube of
about two inches bore, warmed by rubbing, will alternately attract bits of
paper, thread, &c. and drive them from it again.
If
616
BOOK 4
ASTRONOMY
If a piece of iron be laid upon mercury, it will caufe that fluid to be de-
preffed round the edges of the iron: if an oily fubftance lighter than water
be laid thereon, the water in like manner will be depreffed, as if it were
repelled and driven from it: repulfion takes place between fome bodies as
foon as they are ſo diſtant from each other as to be out of the ſphere of the
attraction of coheſion: however, bodies that repell may be brought fo near as
to attract each other: thus, oil and water may be ſhaked together till they
mix: thus alfo, quickfilver by rubbing an amalgama of it made with tin
upon iron, may be made to adhere thereto.
1436 The greateſt inſtance of repulfion is found in the air, the contraction
and expanſion whereof to Sir Ifaac Newton appeared quite unintelligible,
by fuppofing the particles of air to be ſpringy and ramous, or rolled up like
hoops, or by any other means than a repulfive power: optics p. 371. By
reaſon of this repulfion, air is capable of fuch compreffion and dilatation that
it may be ſqueezed fo as to take up but an exceeding fmall part of the
room which it fills in its natural ſtate; on the other hand, it is capable of
being rarified to that degree that only one cubic inch of air, ſuch as commonly
furrounds us near the earth, if all preffure were taken therefrom, would ex-
pand itſelf through the whole orbit of faturn.
Air is thought by Sir Ifaac Newton to confiſt of particles which repell
or fly from one another with a force which is reciprocally proportional to the
diſtance between the centers of the particles. Air, notwithſtanding its elaſticity,
is capable of being fixed to folid bodies of various kinds, and as it were con-
folidated with them; and may again be ſeparated from them, and reſtored
to its natural elaftic ftate. Many ſolid hard bodies confiſt partly of air in a
fixed ſtate, its particles cohering by a ſtrong attraction; but may be ſeparated,
by fire or fermentation, from the body wherein they are impriſoned, and be-
come true elaſtic air: and this air, after being let loofe, may again be abſorbed,
and confolidated with the body from which it was ſeparated.
A cubic inch of heart of oak was found to contain 208 cubic inches of
air, ſuch as we breath near the earth, which air, when contained in the
wood, if it had been in an elaſtic ſtate, would have rent it into ſhivers,
with an exploſion like that of gunpowder: but its particles being in cloſe
contact, and adhering to one another, or to the particles of the wood by at-
traction, conſtituted a part thereof, and was in weight about a fourth part
of the cube of oak. But of all bodies whereon the late worthy Dr. Hales
made experiments, he fays human calculus contains the greateft quantity
of air: fee his vegetable ſtatics, vol. 1. chap. 6.
It
CHAP. 3.
617
ASTRONOMY
It is by attraction that the minute particles of folids are fo cloſely united
to thoſe of fluids, as to make the whole become tranſparent: thus, watery
and earthy particles of various kinds are diffolved in air, and ſuſpended therein :
thus alfo, falt is fufpended in fea water, metals and other heavy bodies in
fuch menftruums as difolve them. See this finely illuftrated in the philofo-
phical tranſactions for 1765, page 146.
1437 Theſe two properties, attraction and repulfion, ſeem to contradi&
what has before been ſaid of matter, that it is void of all activity, is of itſelf
purely paffive, and incapable of all ſpontaneous motion. We have a very clear
apprehenfion that one body or parcel of matter may affect another, as to
motion or reft, by ftriking thereon, fo as to put it in motion if it be at
reſt, or to change its direction if it be in motion: but we can form no
idea how any two parts of matter can act upon each other at a diſtance;
for, then they must be fuppofed to act where they are not: Sir Ifaac Newton
was of opinion that there was diffuſed through the univerſe, at leaſt through
the folar fyftem, a prodigious thin and ſubtle ethereal fluid, by the impulſe
of which upon the folid particles of matter the powers of attraction and
repulfion are made to act; but then it is not eaſy to apprehend how the im-
pulſe of this ethereal fluid fhould always act in fo regular a manner, accord-
ing to fixt and eſtabliſhed laws, as it is found by obfervation and experiments
to do, without the guidance of fome intelligent agent: if therefore we
ſhould attribute theſe powers to the immediate interpofition of the Divine
Being, I can fee nothing in this opinion unworthy of a Chriſtian philo-
fopher: non vacat exiguis rebus adeffe Jovi, might pafs with an heathen,
who imagined it to derogate from the majeſty of the fupreme Lord of the
univerſe to give his attention to fmall matters, or thought the taſk too great
for him to overlook and conduct the whole; and therefore affigned different
deities to different parts of the world, Jupiter to govern the heaven, Ceres
on the earth, Neptune in the fea, &c: but to us who have better inſtructions
concerning the Divine attributes, who have been taught that God is preſent
every where, fills heaven and earth; that nothing can eſcape his knowledge,
or refift his power, that in him and by him, all things animate and inanimate,
move and have their being; it cannot appear unreaſonable to reſolve all at laſt
into his will and pleaſure, as the firſt cauſe of all appearances and effects both
in heaven and earth, and in the infinite ſpace that furrounds them: indeed the
Divine omnipreſence in all times, as well as in every place is ſo much above
our comprehenfion, that it is difficult to find words to exprefs our conception
thereof: what ever we can fay of ſpirit must be borrowed from expreffions
taken from the fenfations of the human mind: Sir Ifaac Newton had ſaid the
Deity
4 K
618
BOOK 4.
ASTRONOMY
·
CC
Deity perceived what ever paffed, fully and intimately, as it were in his fenfo-
rium; this raiſed fome clamour among his adverfaries, which Mr. Maclaurin
has anſwered in a very proper manner; "that the expreffion conveys a very
ſtrong idea of the intimate preſence of the Deity every where, and of his
"perceiving whatever happens in the compleateft manner, without the uſe of
any intermediate agents or inftruments; and that Sir Isaac made uſe
"of it, with this view only; for he very carefully guards againft our
imagining that external objects acted upon the Deity, or that he ſuffers
any paffion or reaction from them." Maclaurin's account of Sir Isaac
Newton's philofophy page 383.
CC
1438 Electricity has employed the attention of a great number of perfons,
in order to inveftigate the properties, the cauſe and effects of it: the theory
thereof is not yet brought to perfection. This I think we may fay is difco-
vered, that there is in many bodies a latent fire confined, which breaks forth
when all compreffion is removed from it: thus, quickfilver in a glaſs bottle
void of air, when fhook, fends forth light, which it will not do in an
open bottle, wherein its furface is preffed upon by the ambient air. Electricity
as well as magnetiſm is thought to be cauſed by the efflux of particles from
the electrical or magnetical body, and their return to it again, carrying along
with them fuch bodies as they meet with. See in Boyle's works abridged,
vol. 1. effluvia: electricity. Newton's optics pag. 314. &c.
In 1709 Mr. Hawksbee publiſhed a book of phyfico-mechanical experi-
ments, feveral of which are electrical: after that, we have many inftances
of the properties of electricity related in the philofophical tranfactions, down
to the preſent time, eſpecially thoſe of late years; wherein an infinite number
of experiments have been made, and ſeveral treatiſes have been written in
divers parts of Europe, by Mr. Franklin, the Abbee Nolet, Mr. Watfon,
Mr. Wilson, &c. See the hiftory and preſent ftate of electricity by Dr.
Priestley, in 4to. printed in 1767 for Dodfley, &c. Here the reader will meet
with a large account of what has hitherto been done by others, or by the
author himſelf; who, befides relating fome experiments of his own, has
given many valuable hints about the defiderata, or things ftill wanted to be
difcovered in electricity; has furniſhed the unpractifed electrician with
inftructions how to proceed in his enquiries, and given a deſcription of an
apparatus, proper for exhibiting the experiments that have been already
made, or for making a farther progrefs in this curious part of natural phi-
lofophy. The greatest utility arifing from what is hitherto known
on this ſubject, is our being able to obviate in fome meaſure the miſchiefs
caufed
CHAP. 3.
619
ASTRONOMY
cauſed by lightning: and to cure fome diſeaſes that will not fubmit to
any other medicine.
Mufchenbrook has a treatiſe about the loadſtone, wherein, after a great num-
ber of experiments, he is forced to own himſelf at a lofs, how to account
for the ſeveral phenomena obferved by him; nor could he diſcover any law
according to which the force of magnetic attraction is diminiſhed by the
diſtance of the iron from the loadſtone: Sir Ifaac Newton, by fome coarſe
experiments judged that magnetiſm decreaſed in about the triplicate ratio
of the diftance, princip. p. 368. But theſe ſpeculations I ſhall not purſue
any farther, as they do not relate to my preſent ſubject.
Remarks upon § 1411.
1439 The definition here given may ſerve well enough for what is called
a fimple pendulum; namely, a ſmall bullet ſuſpended by a fine thread; the
'length whereof may be taken without much error as here deſcribed: when
the weight is of confiderable dimenfions, as thoſe of large clocks are, the
length is taken from the point of fufpenfion to the center or point of oſcil-
lation, which in a globe is below the center thereof, but its diftance from
the center is leſs the longer the ftring is: if the globe be ſuſpended by a
rod, as in common clocks, the weight and length of the rod muft be
taken into the account, in order to find the center of ofcillation; as may
he feen in Hugenius de Horolog. ofcillator. Rowning's natural philoſophy.
and in Graveſande, phyfices elementa mathem. lib. 4. cap. 11.
The common clockmakers who would have their pendulums vibrate
feconds, or half feconds, make them nearly of the proper length, with a
fcrew at the end of the rod, whereby the weight or bob, as it is called, may
be eaſily raiſed higher, if the clock goes too flow; or let down lower, if it
goes too faft, till it keeps true time.
Remarks upon § 1427.
1440 This opinion of Whiston is founded upon conjecture, and was adopted
by him in his hypothefis, mentioned § 1379: and favours ſomething of the
ancient prejudice, that circular motion is the moſt perfect, and that therefore,
that of the heavenly bodies is circular. Though we cannot always affign the
reafons upon which the actions of Infinite Wiſdom are founded, we may
diſcover in this difpenfation the freedom wherewith the planetary motions are
ordered, enough to stop the mouths of all thoſe who would have it that things
4 K 2
are
620
BOOK 4.
ASTRONOMY
are in their prefent conftitution by a neceffity of nature, and could not have
been otherwiſe; or that the whole frame of the univerfe was mechanically
made, by matter and motion; whereas the interpofition of an All-wiſe free
intelligent agent appears, wherever we turn our eyes.
The oblong orbits of comets may feem to fome perfons to have an
awkard appearance; and yet, whatever uſes theſe bodies may have, to us
unknown; one thing manifeftly providential is obvious, that by reaſon of
the various pofitions of their orbits, and the vaſt diſtance to which ſome of
them go, they are not fo liable to diſturb the motions of each other, or the
orbits of the planets. See § 1325 and 1327.
CHAP. 4. THE IRREGULARITIES OF THE MOON'S MOTION
CAUSED BY THE ATTRACTION OF THE SUN.
1441 Sir Ifaac Newton has demonſtrated that, if different bodies revolve
about a common center, and are acted upon by a centripetal force which is
reciprocally as the fquares of the diſtances, then the fquares of their peri-
odical times will be as the cubes of their diftances; and that, if they revolve
in ellipfes, the ſquares of the periodical times are as the cubes of the
axes. princip. lib. 1. prop. 15.
B,
greater
1442 The force of an attracting body is as the quantity of matter thereof,
that is, in direct proportion to the cube of its diameter: if I would compare two
homogeneous globes A and B, ſuppoſe both of lead; the quantity of matter
in A is to the quantity of matter in в as the cube of the diameter of A is to
the cube of the diameter of B: thus, if the diameter of a be 2 inches, and the
diameter of B 3 inches, the cube of 2 is 8, and the cube of 3 is 27; I fay the
weight or quantity of matter in A, is to the weight of в, as 8 to 27. This
propofition may alſo be applied to the fame attracting body at different
diſtances; that its attractive force is directly as the cube of the apparent
diameter thereof feen from the body attracted by it: thus, if the apparent
diameter of the fun be at one time 31, at another time 32, his force when
3 is to his force when 32 as 29791 the cube of 31 to 32768 the cube of 32.
1443 If the earth and moon had no other gravitation befides their ten-
dency towards each other, the moon would perform her revolutions round
the earth, in an ellipfis, always of the fame fize and ſhape, in the fame
periodical time, the line imagined to be drawn from the center of the earth
to the moon deſcribing equal triangular areas in equal times: but the fun,
though at an immenfe diſtance, by reafon of the great quantity of matter
con -
CHAP. 4.
62F
ASTRONOMY
contained in his vaft globe, exerts a confiderable attraction towards the earth FIG.
and the moon, or as it may otherwiſe be expreffed, caufes thoſe bodies to
gravitate towards his center; and this gravitation is of different force, accord-
ing as thoſe bodies are at different diſtances from him. This unequal attraċ-
tion of the fun difturbs the motion of the moon, changes the figure of her
orbit, varies her diſtance from the earth, and prevents her defcribing equal
areas in equal times, as otherwiſe fhe would do, by § 1418.
When the earth and the moon are at the fame diſtance from the fun,
they are both equally attracted; when one of them is farther off from that
luminary than the other, that neareſt to him is moſt ſtrongly attracted:
and it is the difference between them, or the exceſs wherewith one of thoſe
bodies gravitates towards the fun, or is attracted by him more than the other
that is principally to be confidered.
1444 We will first confider the orbit of the moon as if it were a perfect
circle: in fig. 14, let ABCD reprefent the orbit of the moon, wherein fhe is 14
carried round according to the order of the letters: let s be the center of the
fun; the moon at в is in conjunction with the fun, at D in oppofition, at a
and c in quadrature: the moon in quadrature at A or C, is at the fame diſtance
from the fun as the earth at E, and confequently thoſe bodies would be both
equally attracted by the fun, if the attraction were in parallel lines as the dot-
ted lines are; but, as the direction of it is towards the center of the fun, it has
ſome ſmall effect in drawing them nearer to one another, and fo increaſing their
mutual attraction; this brings the moon nearer to us: from the quadrature
A to the conjunction B, the direction of the motion of the moon fhewn
by the ſhort tangents Aa, bb, cc, &c. making acute angles with Es the
direction of the funs attraction, ſhe is continually accelerated: from the
conjunction в to the next quadrature c, fhe is going farther from the fun,
in directions fhewn by the tangents dd, ee, making obtufe angles with the
'funs attraction, and is retarded: all this is obvious and eafy to apprehend; the
greateſt difficulty is to conceive how the like effects of acceleration and retar-
dation ſhould happen in the other half of her orbit: in order to ſee this, we
muft confider, that the diſturbing force of the fun arifes, not fimply from
his attraction of the earth or the moon, but from the difference of the
forces wherewith thoſe bodies are attracted by him: for, if the funs attractive
force always acted equally upon both, the moons velocity might be increaſed
or diminiſhed thereby; but would be ftill equable and uniform: whereas,
in the half of the moons orbit ABC, the moon, being nearer to the fun,
is more attracted than the earth; in the other half CDA, the earth, being
nearer to the fun, is more attracted than the moon; now, to a fpectator
upon
622
BOOK 4.
ASTRONOMY
FIG. upon the earth, who confiders himfelf as at reft, the earth being attracted
nearer to the fun, and farther from the moon, will cauſe the moon to
appear to go farther from the earth, and the motions of the moon will
appear the fame as they would do if the were attracted the contrary way,
by an imaginary fun at P.
The difference or excefs whereby the fun attracts the earth more than
14 the moon all the time the moon is going from the quadrature c to the op-
•
pofition D, where that exceſs is greateft, makes the moon appear to accelerate
her motion, fo as to go fwifteft at D: as he comes from thence the difference
between the force of the funs attraction exerted upon the earth and upon the
moon grows leſs and lefs, and the moons velocity is continually retarded, till fhe
comes to her other quadrature A, where the funs attraction acts with equal
force upon the two bodies: this acceleration and retardation of the moon in
her orbit is called the variation, and was firſt obſerved by Tycho Brahe.
1445 When the moon, from the quadrature immediately following con-
junction, is going to oppofition, the earth, being continually more and more
attracted, takes every day a longer ftride towards the fun, than on the day
15 immediately preceeding: this is fhewn in fig. 15, where in the firſt day the
earth is by the fun attracted from e to 1, in the ſecond day from 1 to 2, in
the third day from 2 to 3, &c. this is one cauſe of the moon appearing then
to accelerate her motion, to the oppofition, and to retard it as fhe comes from
thence to the following quadrature; when the earth recedes from the fun by
the ſame degrees inverted; namely, from 3 to 2, from 2 to 1, from 1 to e.
1446 The velocity of the moon in her revolution round the earth being
changeable as above; cauſes a change in the ſhape of her orbit: when her
projectile or centrifugal force is too ftrong for the centripetal, as is the cafe
when the moon is in fyzygy, where the attraction of the fun weakens the
mutual gravitation between the earth and the moon, by attracting one of thoſe
bodies which is the nearest to him from the other, her orbit is nearer to
16 a ftrait line than in any other part: this is fhewn in fig. 16, where the
black circle repreſents the natural orbit of the moon, that ſhe would go in if
the fun had no effect upon her, and the dotted arcs gb, and mвn, repreſent
the lefs curve parts of a larger circle wherein the attraction of the fun caufes
her to move: for, the greater the velocity of the moon is, the more does the
centrifugal force prevail over the centripetal, and the nearer does her path
grow to a ftrait line. On the other hand, when the moon is in quadrature,
the path fhe goes in is more curve, or part of a circle leſs than her natural
orbit, as is fhewn by the dotted arcs bac, and dce: when the moon is in
the octants, i. e. in the middle between quadrature and fyzygy, the effect
of
CHAP. 4.
623
ASTRONOMY
of the funs attraction is nearly mean, between the greateſt in fyzygy and the
leaft in quadrature. The difference between the black circle and the dotted
orbit is drawn much greater than it really is, in order to make it eaſily
conceived. Sir Ifaac Newton computed the diftance of the moon from the
earth in quadrature to be to the fame in fyzygy as 70 to 69, princip.1. 3. p. 38.
Here, before the reader proceeds any farther, it will be proper for him to
go back to § 951, and read on to the end of the chapter.
1447 The orbit of the moon being an ellipfis not much different from
a circle, the earth, or to be more accurate, the common center of gravity
of the earth and moon being in one focus thereof, what has been faid of the
circular orbit, § 1444, 1445, will be found true in the ellipfis, cæteris paribus;
namely, I, that the motion of the moon is ſwifteft in fyzygy, floweſt in
quadrature; 2, that from conjunction her motion is retarded all the way to
the following quadrature; 3, that from thence it is accelerated all the way
to her oppofition; 4, that from the oppofition it is retarded all the way to
the fubfequent quadrature; and 5, that from thence it is accelerated all the
way to the next conjunction.
1448 The fhape of the moons elliptical orbit is alſo ſubject to like changes
as we have ſuppoſed in a circular orbit; the natural ellipfis of the moon, which
fhe would deſcribe round the earth, without the action of the fun, is by the
funs attraction made more curve when the moon is in quadrature; lefs curve
when the is in fyzygy; for in quadrature the centripetal force of the earth
has its full force, and is a little increaſed by the funs acttion: in fyzygy
the funs action diminiſhes the natural gravitation between the earth and the
moon, by attracting the neareſt of thofe bodies from the other; fo that, the
centripetal force being less than it would be, and the projectile force increaſed,
the moons path becomes lefs curve, or nearer to a ſtrait line than it otherwife
would have been: in the octants the effect of the funs attraction is mean,
between the greateſt and the leaft; and therefore does not alter the ſhape of
the moons ellipfis, or the velocity of her motion.
1449 The apogee and perigee of the moon are the two extream points of
the line of the apfides: when the moon is in the apogee, the line of the di-
rection of the centripetal force is perpendicular to the tangent, or the line
wherein the projectile force impells the moon; and, if the two forces were
adequate, ſhe would go round the earth in a circle, at her greateſt diſtance,
with an uniform velocity: but, having been continually retarded in her
motion, by the attraction of the ſun and the earth, and the projectile force
having been continually diminiſhed all the way in coming to the apogee;
the centripetal force there prevails, and brings her nearer and nearer to the
earth,
624
BOOK 4
ASTRONOMY
FIG. earth, all the way till fhe arrives at her perigee: there the line of direction
of the centripetal force is again perpendicular to the tangent, or path of the
moon, wherein the projectile force impells her; and, if the two forces were
adequate, the moon would now, with an uniform velocity, go round the
earth in a circle, at her leaſt diſtance; but the centripetal force having been
continually increaſed in her deſcent from the apogee, has, by cooperating
with the projectile force, made the fame too ſtrong for the centripetal, fo
as to cauſe the moon to go farther and farther off, with a retarded motion,
and a velocity continually diminiſhed, to the apogee, &c.
When the line of the apfides and the moon are both in fyzygy, the
velocity of the moon is greater than when they are in quadrature; becauſe
the fun then attracts the moon when in conjunction, and makes her run
fafter towards him; and attracts the earth from the moon when ſhe is in
oppofition, which lets the moon go with greater velocity, and run farther
on, before fhe is turned by the centripetal force of the earth; then the
17 apogee goes forward from A to a, as is feen' in fig. 17, where the black
ellipfis fhews the natural orbit of the moon, wherein the line of the apfides
is AP,
the apogee would be A, the perigee P; whereas the attraction of the
fun cauſes her to run farther out in the dotted arc wherein ſhe does not
come to her apogee before fhe gets to a: the line of the apfides will be
ap, the
the
apogee will have moved forward from A to a, the perigee from P to p.
1450 The moons apogee or the place of her greateſt diſtance from the
earth does not always point towards the fame ftars in the heaven, as it
would do, if the longeſt axis of her ellipfis continued parallel to it ſelf;
which would be the cafe, if the attraction of the fun did not diſturb it:
when the longer axis of the moons ellipfis is in fyzygy, or points towards
the ſun, and the moon is alſo in fyzygy, the attraction of the fun increaſes
the velocity of the moon all the way to the ſucceeding quadrature and makes
the moon in apogee run farther out from the earth; fo that ſhe goes farther
before ſhe arrives at the fituation mentioned § 1449, wherein the line of direc-
tion of the centripetal force is perpendicular to the tangent or line of projectile
force, and is the apogee, where the centripetal force prevails, as has juft now
been faid: here the apogee goes forward. On the other hand, when the line
of the apfides is in quadrature, the contrary falls out; the longeſt axis of the
moons ellipfis is ſhortened, and the ſhorteſt axis lengthened, by the funs attrac-
tion; and the moon comes fooner to the fituation wherein the line of centripetal
force is perpedicular to the tangent, than fhe would have done without the
funs action: fo that in this cafe the apogee goes backward: thus, in every
lunation or fynodical month, the moons apogee goes forward in the fyzygies,
back-
CHAP. 4.
625
ASTRONOMY
backward in the quadratures, but goes forward more than it goes backward: FIG.
becauſe, when the apogee and the moon are in quadrature, the attraction of
the fun has only a ſmall tendency to bring the moon nearer to the earth; this
increaſes the centripetal power of the earth, increaſes the curvature of the
orbit, and makes the moon come fooner to the apogee; that is, the apogee goes
backward: whereas, when the apogee and the moon are in fyzygy, the
attraction of the fun diminiſhes the centripetal force, and the path of the
moon is leſs curve; then the apogee goes forward: the force that carries it
forward in fyzygy is computed by Sir Isaac Newton, to be double to that
which carries it backward in quadrature: fo that, upon the whole, the former
motion fo much exceeds the latter, as to carry the apogee round the zodiac,
according to the order of the figns, in about nine
years.
In fig. 18, the black ellipfis fhews the natural orbit of the moon when 18
the line of the apfides is in quadrature: in this fituation, the attraction of
the fun ſhortens the longeſt axis of the elliptic orbit, lengthens the ſhorteſt,
the moon comes nearer to the earth, moves in the dotted curve, and gets
fooner to her apogee in a; fo the apogee appears to go back from A to a.
Scholium. When the apogee goes forward or backward, the perigee does
the fame: aftronomers take notice chiefly of the apogee; becauſe the moons
place, or as it is uſually called the moons anomaly, is meaſured from thence,
and is the diſtance of the moon from the place of her apogee, in degrees
minutes and ſeconds, reckoned according to the order of the figns.
The moon has been confidered as moving in an ellipfis, for the fake of
more eafily conceiving her motion, and reducing it to a computation, in or-
der to find her place at any time: whereas, in reality, her path is perpetually
changing, in ſuch a manner, that ſhe may every minute be faid to be moving
in a part of an ellipfis, in fize, ſhape, and fituation, different from that fhe
was defcribing in the minute immediately preceeding.
1451 That the moon goes farther before fhe comes to her
apogee, the
greater the projectile force is in proportion to the centripetal, may be illuf-
trated by fig. 19, wherein if we conceive a ball to be ſhot out of a gun, if it 19
met with no obſtruction, it would go on for ever in a ſtrait line ABC, if acted
upon by that impulfe alone; but being all the while attracted towards the earth,
the centripetal force operates continually upon it, and cauſes it to defcribe a
parabola, the vertex whereof at D is the place where it begins to fall towards
the earth, and is as it were the apogee of the ball, or the greateſt diſtance
from the earth to which the impelling force can carry it, before it falls: it
is eaſy to ſee that, if the projectile force had been greater, the ball would have
been carried farther as to E, before it would fall; and if the projectile had
4 L
been
626
BOOK 4.
ASTRONOMY
FIG. been lefs, the fame centripetal force would cauſe it to fall fooner, as when it
was got no farther than B: fuch is the cafe of a projectile near the earth; that,
becauſe the centripetal force remains the fame, the vertex of the parabola
deſcribed thereby, is farther from the point of impulfe, the greater the im-
pelling force is: the like obtains in the moon, with this difference only; that
befides the projectile force, the funs attraction, fometimes accelerating, at
other times retarding the fame, the centripetal force of the moon towards
the earth is alfo in fome fituations increaſed, in other fituations is diminiſhed,
by the attraction of the fun, whereby the apogee is puſhed forward, or
drawn a little backward, as has been faid.
20
1452 In fig. 20, the great circle reprefents the orbit wherein the earth
goes round the fun at s: the ſmall ellipfes are ſo many orbits wherein
the moon is carried round the earth at E: the line of the apfides or longeſt
axis of the moons orbit is AP, the apogee A, the perigee p: the line of nodes
mn: if we take m for the afcending node and 2 for the defcending node, it
is eaſy to apprehend that one half of the ellipfis man is above the plane of ·
the earths orbit; the other half mp n below it: that A is the moons northern,
P her fouthern limit: if the line of the apfides and the line of the nodes were
always carried parallel to themſelves as in this figure, they would each point
towards the fame ftars; becauſe the diameter of the moons orbit, and indeed
of the orbit of the earth, carried to the heaven is infenfible, too ſmall to be
obſerved: but what we have here ſuppoſed, in order to make a difficult affair
more eaſy to be apprchended, is not true: neither the line of the apfides,
nor the line of the nodes are carried parallel to themſelves.
1453 The moons orbit being in a plane different from the plane of the
ecliptic, whereof the fun always occupies the center, his attraction has a ten-
dency to bring the moons plane nearer to the plane of the ecliptic. When
the plane of the moons nodes extended paffes through the center of the
fun, his attraction cauſes no change therein, and fhe may then be faid
to be in her natural plane: the only effect the fun can then have upon the
mòon, is to accelerate or retard her motion, as mentioned § 1444, 1445,
1447: in every other fituation of her orbit, the attraction of the fun brings
the moon, and confequently the plane ſhe moves in, nearer to the ecliptic;
that is, makes her latitude lefs than it would be if the fun ceaſed to act
upon her.
1454 One effect of the funs attraction is to change the fituation of
the line of nodes: for, as the moon is approaching to any node, the attraction
of the fun makes her come fooner into the plane of the ecliptic, or to her
node, than without the funs action fhe would do.
When
CHAP. 4.
627
ASTRONOMY
When the line of nodes nm is in fyzygy, the plane of the moons orbit FIG.
continued paffes through the center of the fun, and confequently his at- 20
traction cauſes no alteration in the pofition thereof: the angle of inclination
between the orbit of the moon and the ecliptic is then the greateft poffible, and
the nodes are at reft: in every other fituation of the orbit of the moon, the
fun is on one fide thereof, and fo attracts the moon as to bring her nearer
to the ecliptic, and thereby to leffen continually the angle between the two
planes of the moons orbit and of the ecliptic, all the way till the line of
nodes is in quadrature with the fun, when that angle is the leaſt it can be:
from thence forward, as the fun approaches to the node again, this attraction
of the moon towards the ecliptic brings her fafter towards the plane thereof,
at every approach to the node; by which means, the angle between the two
planes grows wider, and wider till the line of nodes comes to the next fyzygy,
where it is again of its natural magnitude.
In fig. 21, let EDC be part of the ecliptic, s the fun, AB part of the 21
moons orbit, wherein the would, without the funs attraction, have come
to her node at c; and the angle between the two planes would have been
ACE; by the attraction of the fun at s, fhe will come fooner to her
node at D, and the angle between her orbit and the ecliptic will be ADE,
wider than ACE.
The nodes are at reft when they are in fyzygy, and are, in moſt other
fituations, with more or lefs velocity, retrograde, and go back faſteſt in
the quadratures: when the moon is between the node and the neareſt quad-
rature, the nodes go a very little forward; but in every other fituation,
backward. Newton princip. 1. 3. prop. 30. The refult is, that in every
lunation they are carried backward; fo as to go round the zodiac, contrary
to the order of the figns, in about 19 years.
1455 When we ſpeak of the apogee or the nodes going forward or back-
ward, by means of the funs attraction, we are not to think the action of the
fun can operate upon the line of the apfides, or the line of the nodes, or
upon the plane of the moons orbit; theſe are all of them imaginary unreal
beings, terms invented by aftronomers, for the more eafily conceiving and
explaining the motions of the moon: the attraction of the fun can only act
upon the moon as a ſolid body, and accelerate or retard her motion, or
change the direction thereof, and thereby cauſe her to change her orbit, to
come fooner or later to her apogee, or to her node: the action of the ſun upon,
the earth alfo, as a folid body, may by attracting it out of its place, caufe
the like changes in the moons apparent motion, as the earth is the place
from whence we always view that planet.
4 L 2
I
To
628
BOOK 4.
ASTRONOMY
FIG.
2.2
To illuftrate this by two examples; 1, fuppofe at any time the moon comes
to her apogee when her longitude is in the first point of r; in the fame
month of the fubfequent year, fhe will not come to her apogee till fhe is got
to the 10° of 8; we fay then, that the apogee has in that time gone 40° forward:
2, ſuppoſing the afcending node of the moon is on this preſent 20th of may
in the 20° of 8, we fhall, on the fame day of the fame month in the next
find that node about the 1° of 8; on which account, we fay the line
year,
of nodes has gone backward at the rate of about 19° in a year; and confe-
quently, is carried quite round the zodiac in about 19 years.
1456 The inclination of the plane of the moons orbit, cæteris paribus, is moſt
diminiſhed by the funs attraction when the moon is in her north or fouth
limit; for then the attraction is moft direct, that is, neareſt to perpendicular
to the path of the moon: the force of that attraction is more and more
oblique, and therefore is more and more diininiſhed, all the way as the
moon goes from the limit to the node, where the funs attraction ceafes to
change the inclination of the orbit, and it is restored to its natural ſtate.
In fig. 22, let SE repreſent part of the ecliptic, PL the plane of the
moons orbit, ſuppoſing them both to be viewed edgewife, P the place the
moon would be in when at her northern limit, if the fun had no effect
upon her motion, then her apparent place in the heaven would be at A; and
the angle between the plane of the orbit of the moon and the plane of the
ecliptic would be PNS: but, the attraction of the fun drawing the moon to Q,
the angle between thoſe two planes will be QN S, and the moons apparent place
in the heaven will be at B. The fouthern limit of the moon without
the funs action would be L, but the fun attracting her to /, fhe appears in the
heaven at R; and the angle between her orbit and the ecliptic will be E N .
When the earth is by the fun attracted out of its place, to a fpectator upon
the earth, the moon muſt be ſeen in the heaven, in a place different from that
fhe would have appeared in, had the earth not been acted upon by the fun. It
is obvious to fee, that the angle between the ecliptic and the orbit of the moon
grows lefs and leſs, all the way as the line of nodes is going from fyzygy to
quadrature; and, that the fame angle is increaſed, all the way that line is
going from quadrature to fyzygy.
1457 The more oblique the direction of the funs attraction is to the path
of the moon, the weaker is the force thereof; the nearer to perpendicular to
the moons path the funs attraction is, the ſtronger is the attracting force:
the force of attraction, like that of impulſe, is as the fine of the angle the
line of direction makes with the plane attracted.
1158
CHAP. 5.
629
ASTRONOMY
1458 The ſmall ſyſtem of the earth and moon is neareſt to the fun when
the earth is in perihelion; therefore, the difturbing force of the fun, as to all
the irregularities above mentioned, is then greateft; his diſturbing force is
leaſt when the earth is in aphelion, at the greateſt diſtance from the ſun: the
earth is in perihelion in december. It has already been faid, § 1450; that,
when the moon is in fyzygy, the centripetal force is more weakened by the
attraction of the fun, than it is increaſed thereby in quadrature; one confe-
quence of this increafing is, that the projectile force becomes too ſtrong for
the centripetal, and the more fo, the greater the funs attraction is: the projectile
force being ſtronger caufes the moon to go in an orbit larger, as being nearer
to a ftrait line; and, going in a larger orbit, ſhe muſt take longer time to
go through the fame number of degrees: in winter, therefore, when the fun
is neareſt, and his attractive force ſtrongeſt, the periodical month is a little
longer than in fummer, when the earth is farther from the fun, and his
attraction weaker.
CHAP. 5. THE TIDES.
1459 Tide in ancient Engliſh fignified the fame as time does, as appears
by thoſe compound words noon-tide, even-tide, ſhrove-tide, &c. by the tide
in general is now meant the flux and reflux of the fea; the firſt of which is
the tide of flood, or high water; the latter is the tide of ebb, or low water.
That the tides are influenced by the moon, has long been known: Kepler
was the firſt who thought they were caufed by the gravitation of the
water towards that planet: Sir Ifaac Newton entered deeply into that ſpecu-
lation, and demonftrated in what manner the tides were raiſed, by the
attraction of the fun and moon; principally by the latter, which, though
vaftly inferior to the fun in quantity of matter, is much fuperior to him
in raifing the tides, by reaſon of her being fo much nearer to the earth
than that great light is.
If either of the luminaries, or both of them were vertical to one of
the poles of the earth, the water by gravitating towards the fame would
be there accumulated under them, and remain conſtantly at the ſame hight
without any flux or reflux.
1460 We will confider what effect the moon has in the first place. If the
earth and moon were without motion, and the earth were all over covered
with water, the attraction of the moon would raiſe it up on an heap, in that
part of the ocean to which the moon is vertical; and there it would always
con-
630
BOOK 4.
ASTRONOMY
FIG. continue; but, by the rotation of the earth, and the revolution of the
moon, different parts of the ocean come fucceffively under the moon; the
eaſtern parts firſt, which are fucceeded by thofe more wefterly: now the
water being held to the earth by the attraction thereof, or by its gravity,
cannot follow the motion of the moon, fo as to be conftantly in an heap
under her; but takes time to roll over the earth.
23
a,
1461 Let us firſt ſuppoſe the moon to be in the equator: let fig. 23, re-
preſent the earth all over covered with water, as it would appear projected
upon the equator ABCD, the eye of the fpectator being in the axis of the
earth, produced or lengthened to a confiderable diſtance: let abcd repreſent
the orbit of the moon; if the moon be at a, by the rotation of the earth
according to the order of the letters, the meridian A, will come firſt under
the moon, then D, C, B: now as the water is carried round upon the earth
from D, a place in quadrature with the moon, towards A, which may be faid
to be in conjunction with the moon; the motion thereof, will by the attrac-
tion of the moon be accelerated upon the earth, and run faſter towards a
than the rotation of the earth would carry it, and being accelerated will by
continual addition of new force have acquired the greateft velocity at A:
as the water goes from A to B, its running round upon the earth will
be retarded by the attraction of the moon, all the way to B, where confe-
quently it will have the floweft motion: but, if it moves ſwifteft at A
towards B, and floweft at B, the effect must be to raiſe it higheft in the
middle between thofe two places; and the high water will be at M,
whereof the moon paffed the meridian fome hours before. The tide of flood
is not raiſed inſtantaneouſly, upon the moons coming to be vertical to a
place, but, by a gradual acceffion of new force, the following waters puſhing
and driving on thofe before, continues to increaſe the hight, and this for
3 hours, fome times 4 or 5 hours or more, after the appulfe of the moon
to the meridian.
In the fubfequent twelve lunar hours, while the water goes through B CD,
as it is carried by the rotation of the earth from в to C, it is attracted the
fame way by the moon at c, and is thereby fo accelerated as to go with
the greateſt velocity at c: from c to D it is retarded, and goes floweſt at D;
and confequently, will be accumulated in the middle between c and D,
and the high tide will be at m. We may confider hours as lunar or folar: the
twenty four lunar hours, are the time wherein the moon goes from a meri-
dian and returns to the fame again: by the twenty four folar hours are meant,
the time between the funs appearing to leave any meridian and returning to
the fame. As the moon, by reafon of her progrefs in her orbit, comes every
day
CHAP. 5.
631
ASTRONOMY
day ſeveral minutes later to the meridian than ſhe did the day immediately Fic.
preceding, the lunar hours are a little longer than the folar.
1462 I have here fuppofed the moon to be in the equator, where her at-
traction has the greateft effect; becauſe, there it moſt accelerates or retards
the rolling of the waters along, in the earths rotation: in all other fituations,
the force of the moon is weaker; becauſe the attraction is in a more oblique
direction, and the farther the moon is from the equator, the more oblique is
her attraction, and the weaker is the force thereof. In fig. 24, let E nos be 24
the globe of the earth, EQ the equator; if the moon be at L, ſhe
accelerates the water coming directly towards her, or retards what is going
directly from her, the moſt that is poffible: if the moon be at в or K, fhe
attracts the water in an oblique direction, and more oblique, the more ſhe
is diſtant from the equator.
The obliquity of the direction is not the only cauſe of the tides being leſs
when the moon is out of the equator; for, when the moon is at a diſtance
from the equator, the greater her declination is, the nearer does the cafe ap-
proach to her being over one of the poles, where it has been faid § 1458,
the water would be raiſed on an heap without reciprocation of high and
low tide.
1463 The fun has alſo an influence upon the tides, as well as the moon,
though not in the fame degree: Sir Ifaac Newton has computed that the
force of the moon in the great ocean raiſes the water ten feet; whereas the
fun only raiſes it two feet: when thefe luminaries are in fyzygy, and
in the equator, the combined forces of both raiſe the tide twelve feet,
when the moon is in quadrature with the fun, and both thoſe luminaries are
in the equator, the attraction of the one raiſes the water where the other
depreffes it; and, the leſs force of the fun being deducted from that of the
moon, the tide will be no more than eight feet.
Thus it appears that, though the two luminaries excite two motions, they
will not appear diftinctly; but, between them will arife one mixed motion
compounded out of both.
1464 The force of the moon to move the ſea is found by knowing what
proportion it bears to the force of the fun, and this is collected from the
effects of thofe forces. Before the mouth of the river Avon three miles below
Briſtol, the water has been obferved, in the vernal and autumnal fyzygies,
to riſe about 45 feet, but in the quadratures to 25 feet only: the former of
theſe hights ariſes from the fum of the forces of both luminaries, the latter,
from their difference.
What
632
BOOK 4
ASTRONOMY
What has been faid of the general phenomena of the tides, holds true
only in fuch fhores as lie expofed to the wide and deep ocean: as to narrow
or fhallow feas, or the mouths of rivers, the times of high and low water
depend upon feveral circumſtances now to be mentioned; if the water in
flowing towards the fhore paffes over flats or fhallow places, or rocks near
the furface of the fea, by the failors called breakers, the time of high water
will be later than otherwife it would have been without thofe obftructions.
In fuch fhores as lie towards a deep and open fea, with a ſteep afcent,
where the waters can rife and fall without any precipitation of influx or efflux,
the tides anſwer to the forces of the fun and moon: whereas, in fome ports,
by reaſon of their going through long and narrow ftraits, the waters are hur-
ried in and out, with fuch violence, as fometimes to lay the ſhores under
water, for many miles; fometimes to leave them dry for as large a ſpace:
this may happen when a large body of water is raiſed in one or more wide
places, and driven towards a narrow channel which cannot diſcharge them
fo faſt as they come in, fo that the following waters preffing upon thoſe
before, raiſe them to great hights, as was mentioned § 1460.
1465 The greateſt tides fall out in the fyzygies at or near the equinoxes,
when both luminaries are in the equator; which will be the greateſt of all
if the moon be at the fame time in perigee. If the moon be in perigee at the
conjunction, the muſt be in apogee at the immediately preceding and ſub-
fequent oppofition; for this reafon two high tides do not immediately follow
one another. Newt. princip. lib. 2. prop. 24, 26, 27.
1466 The force of the fun or moon in raifing the fea is greateſt on the
appulſe of the luminary to the meridian of the place; but the force impreffed
upon the fea at that time continues a little while after the impreffion, and is
increaſed by a new, though a lefs force ſtill acting upon it: this makes the
ſea riſe higher and higher, till the new force, gradually diminiſhing, becomes
too weak to raiſe it any more; then the ſea is riſen to its greateſt hight: this
comes to paſs in one or two hours, but more frequently in three hours, or
even more where the fea is fhallow. Newt. princip. lib. 3. prop. 24.
When any power is continually increafing, it does not arrive at its
greateſt force till it ceaſes to increaſe: for this reaſon, the heat in fum-
mer is not greateſt at the ſolſtice, when the heat of the fun is greateſt;
but afterwards, when the additional heat being every day lefs and leſs, is
diminiſhed to nothing: fee § 771, 772, 773.
1467 The wind blowing the fame way the tide is going, will both accele-
rate the time of high and low water, and make it alſo riſe to a greater hight,
or run off to a lower ebb: on the other hand, a contrary wind will both
retard the tide and diminiſh the riſe and fall thereof.
1468
Um
Page 625
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Book IV
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CHAP. 5.
633
ASTRONOMY
1468 The action of the luminaries, eſpecially of the moon, having force
enough to raiſe and depreſs the waters of the ſea, muſt have a confiderable
influence upon
fuch a fluid as the air that ſurrounds us, and cauſe a kind of
tide in the atmosphere: the effects of this may be fometimes gentle winds,
and when more violent, ftorms and hurricanes, which are obferved to rage
moſt near the equinoxes. The leffening the weight of the air in
fome places, and increaſing it in others muſt cauſe fome change in the
fluids of animals; accordingly, it is obſerved by phyſicians, that ſome diſ-
eaſes, to which the human body is ſubject, are exaſperated or mollified in
their ſymptoms, in different fituations of the moon: of which ſee Mead
de imperio folis et lunæ in corpus humanum.
1469 Previous to the explaining the cauſe of the tides, Sir Ifaac Newton
laid down fome corollaries, which follow from what he had demonftrated
concerning the irregularities of the moon arifing from the action of the fun:
ſuppoſe, ſays he, the earth had revolving round her feveral fluid bodies, at
equal diſtances from her ſurface, each of thoſe would fuffer the ſame change
in its motion as the moon has been fhewn to be liable to; would move fwifter
in conjunction or oppofition with the fun, and flower in quadrature: fuppofe
farther, thoſe bodies to be fo numerous as to be contiguous, and form a fluid
ring; the attraction of the fun would cauſe thoſe parts of the fluid to riſe
which are in conjunction, and the parts in quadrature to ſubſide: the nodes
alſo of the ring would be retrograde, as the nodes of the moon are found
to be: ſuppoſe farther, that the earth were extended on each fide of this ring
fo as to form a channel to receive it; in the diurnal rotation, every part
thereof by its gravity adhering to the earth, would be carried round
therewith uniformly, if not diſturbed by the action of fome other body:
but by the attraction of the fun or moon the water would be accelerated
coming into ſyzygy, and retarded going into quadrature; and this would
caufe a reciprocation of flux and reflux. princip. lib. 1. prop. 66. cor. 19.
Suppoſe the fluid ring to become folid, as it would be if frozen to ice;
there would indeed then be no more flux and reflux: but if the ring were
looſe, the nodes thereof would ſtill go backward: fuppofe the globe to ſwell
fo as to adhere to the infide of the now folid ring; the cafe would be ſtill
the fame; the nodes of the ring would go back, but more flowly, becauſe
it muſt now carry along with it the weight of the earth.
The ring, not adhering to the globe, would have the greateſt angle
between the plane thereof and the plane of the orbit wherein the globe
revolves, when the nodes are in fyzygy: the ring has a tendency to diminiſh
that angle all the while the nodes are going into quadrature: and will
4 M
impreſs
634
ASTRONOMY
BOOK 4.
1
imprefs this motion upon the globe when it adheres thereto: the globe retains
this motion till the ring gives it an impreffion the contrary way: the greateſt
tendency to leſſen the angle is when the nodes are in quadrature, confequent-
ly, the angle, continually diminiſhing, is leaft when the nodes are in the
octants following quadrature: the tendency to widen the angle being great-
eſt when the nodes are in fyzygy, the angle becomes wideft in the octants
following the fyzygy. See the latter end of § 1466. This leads to the
fubject of the following chapter.
CHAP. VI. THE PRECESSION OF THE EQUINOXES: THE NUTATION OF
THE POLES.
1470 We have ſeen in the preceding chapter how the action of the fun
upon the moon caufes a retrograde motion in the line of nodes. How the
preceffion of the equinoxes follows from the fame principles, I fhall take
the liberty to fhew in the words of Maclaurin, p. 350, of Sir Ifaac Newton's
diſcoveries, as I cannot invent better.
<<
"If a planet revolved about the earth near to its ſurface, in the plane
"of the equator, its nodes would alſo go backward, though with a ſlower
"motion than thofe of the moon, in proportion as its diſtance from the
"earth's center was less than that of the moon. Suppofe the number of
"fuch planets to be increaſed till they touch each other, and form a ring in
"the equator, the nodes of this ring would go backward, in the fame man-
ner as the nodes of the orbit of one planet revolving there. Suppofe then
this ring to adhere to the earth; its nodes would ftill go backward, but
" with a much flower motion; becauſe the ring muſt move the whole earth
"to which it is ſuppoſed to adhere. The elevation of the equatoreal parts of
"the earth has the fame effect as fuch a ring would have; only the motion
" of the nodes of the equator, or of the equinoctial points is flower, becauſe
"the accumulated parts of the earth, above a ſpherical figure, are diffuſed
"over its furface, and have a lefs effect than if they were all collected in the
plane of the equator, in form of a ring. The moon has a greater force on
"this ring than the fun; becauſe of her leſs diſtance from the earth; and
they both contribute to produce the retrograde motion of the equinoctial
points: the motion, however, produced by both is fo flow, that theſe
points will not finiſh a revolution in lefs than 25000 years." Sir Ifaac
Newton has determined the quantity of this motion from its caufes, and
found it confonant to the obſervations of aſtronomers.
<c
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1471 How
CHAP. 6.
635
ASTRONOMY
1471 How the fun being in the center of the ecliptic, by perpetually FIG.
drawing the equatoreal ring into the plane of that circle, cauſes the preceffion
or regreffion of the equinoctial points, is eaſily apprehended, from what has
been faid: how the moon alfo contributes towards this will appear, if we
confider that, though the orbit of the moon deviates from the plane of the
ecliptic, that deviation is but ſmall, only about 5 degrees, fo that, the
attraction of the moon has nearly the fame effect as it would have if her
revolution were in the plane of the ecliptic: and, by reaſon of her near-
neſs to the earth, ſhe has a greater influence in caufing the preceffion of
the equinox than the fun has. From the combined force of both lumi-
naries, the going back of the equinoctial points is found to be at the rate
of
50 feconds in a year: this is the mean motion of the equinoctial points,
as diſcovered by comparing ancient obſervations with modern ones: Brad-
ley fettled it by comparing his own obſervations with thoſe of Tycho Brahe
and others. Phil. tranfact. 1748.
?
1472 From this ring fuppofed round the equator, or from the fhape of
the earth equivalent to ſuch ring, by the theory of gravity, it is concluded
there muſt be twice every year a nutation of the poles, or a change in the
fituation of the axis of the earth: fig. 25 is a perſpective view of the orbit of 25
the earth, wherein it is carried round the fun, n the north pole, s the
fouth pole, eq the ring upon the equator; A is the place of the earth at
the vernal equinox; c the place thereof at the autumnal: at both equinoxes
the plane of the ring extended paffes through the fun; and, there is then no
change in the poſition of the earths axis: when the earth is at в, at the
ſummer folftice, the direction of the funs attraction is towards the upper fide
of the ring, and has a tendency to lift it up, and move the axis of the earth
into the fituation expreffed by the dotted line, nearer to a perpendicular to
the ecliptic, then the north pole has a nutation or nodding towards the fun:
when the earth is at D, the winter folſtice, the attraction is directed towards
the lower furface of the rings plane, and pulls it down, which caufes a
change in the fituation of the axis fimilar to the former, then the fouth pole
has a nutation towards the fun; both theſe nutations caufe the fame change
in the axis of the earth, but are fo finall as to have all along efcaped the
obſervation of aſtronomers, on which account the axis of the earth is com-
monly faid to be carried parallel to itſelf in its annual motion.
1473 If we confider the plane of the equatoreal ring, we fhall find the
moon is fometimes in that plane continued, that is, has no declination; and
fometimes goes into declination, or is elevated above the plane of the ring
feveral degrees. When the moon is in the plane of the ring, her attraction
4 M 2
caufes
636
BOOK 4.
ASTRONOMY
caufes no change in the fituation thereof; when the moon is elevated more or
lefs above the ring, her attraction is more or leſs ſtrong, according to her
different elevation: the nearer to a perpendicular to the plane of the ring the
direction of attraction is, the greater is the force; the more oblique the di-
rection is, the weaker is the force of attraction, § 1457. As the moon goes
from the equator, her attraction grows ftronger till fhe comes to her greateſt
declination, when her attraction is ſtrongeſt: in going from her greateſt
declination nearer to the equator, her attraction grows gradually weaker.
In every revolution of the moon her attraction is ſtrongeſt when ſhe is
in or near the folftitial colure; for then her declination is greateſt: this
change falls out every month; but the nutation cauſed thereby is too ſmall
to be obſerved: in the courfe of 18 years and 7 months there is a change
in the greateſt declination of the moon, which caufes a change of 18″ in
the place of the pole.
1474 When the afcending node of the moon is in the beginning of r,
her greateſt declination from the equator is 28°: when the aſcending node of
the moon is in the beginning of, her greateſt declination is but 18°: the
fine of 28° is 4694716, the fine of 18° is 3090170: the force of the moons
attraction, when the afcending node is in v to the force when her aſcend-
ing node is in, is as 4694716 to 3090170, or in fmaller numbers,
nearly as 47 to 31. § 1457.
1475 In the philofophical tranſactions for the year 1748, Dr. Bradley
communicated to the R. fociety his obfervations of above 18 years, whereby
he diſcovered the nutation of the poles and the quantity thereof: he found
there was 18″ difference between the fituation of the north pole of the
equator in 1726, at the time when the moons afcending node was in the
beginning of aries, and the fituation of the fame pole in 1735 when that
node was in the beginning of libra: the ſtar chiefly made ufe of was that
marked y in the conftellation of draco; this ftar changed its declination 18′
in that interval, or was 18″ nearer to the pole, that is, fo much did the
nutation bring the pole nearer to the ftar, at one of thoſe times than at
the other: for, in order to be affured that this was not owing to any
change of place in that ftar, he obſerved the like change of place in fome
other ſtars: and, by a ſeries of obſervations, during an entire revolution
of the moons nodes, it appears, that from the time when the aſcending
node of the moon was in the beginning of aries, to the time when it was
gone back to the beginning of capricorn, or in 4 years, the pole had
changed its place 9"; and that at the end of 9 years, when the afcending
node of the moon was gone back to the firſt point of libra, the place of
I
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Page 637
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CHAP. 6.
637
ASTRONOMY
the pole was changed 18": and, moreover, at the end of 18 years, when FIG.
the moons afcending node returned to the beginning of aries, the pole had
returned to the place it ſet off from.
In order to explain this, fee fig. 26, where the large circle reprefents the 26
folſtitial colure, on the plane of which are projected in ſtrait lines the plane
of the ecliptic E c, of the equator A B, the orbit of the moon mn, the equa-
toreal ring ab; all viewed edgeways, by the eye in the line of nodes at an
infinite diſtance from r; the moon at m is in the greateſt fouth, at n in the
greateſt north declination ſhe can ever have; her attraction upon the fouth
plane of the equatoreal ring at a is the neareſt to perpendicular, and there-
fore the ſtrongeſt, § 1457, and cauſes the greateſt change in the axis of the
earth, carrying it into the fituation expreffed by a dotted line, and makes the
pole to have a nutation towards the zenith, or a ſtar near the ſame, where-
by the declination of the ſtar is altered, fo as to be a few ſeconds lefs.
In the 27th figure is exhibited the projection of the fame circles on the 27
folftitial colure, as in the preceding figure, viewed in the line of nodes
at an infinite diftance from : here the orbit of the moon mn makes a
fmaller angle with the equator, and confequently the moon attracts with
lefs force, which caufes a nutation of the pole the contrary way to that of
the 26th figure, this was the cafe in the year 1735; when the place of the
pole was 18″ diſtant from the place thereof in the year 1726. I have in
both figures repreſented the deviation of the pole much greater than the
truth, to make it more eaſily ſeen.
In all theſe obſervations Bradley made allowance for the aberration of
the ſtars, and the mean preceffion of the equinox.
Small changes are diſcovered beft by a teleſcope in a perpendicular pofi-
tion, becauſe a ſtar's diſtance from the zenith muft vary as the nutation of
the axis of the earth changes the place of the zenith: whereas, in other
fituations, we cannot be fure the bending of the inftrument, the inaccu-
racy of the divifions, or the uncertainty of refraction, are not fome of
them the cauſe of alterations that are only of a few ſeconds.
As I had fome acquaintance with Dr. Bradley, having been with him at
Kew, at the houfe of the Hon. Samuel Molyneux, Efq; when he was affifting
him in preparing a large ſpeculum for a reflecting teleſcope; I made him a
vifit at Wanſtead in Effex, while he was making the foregoing obfervations:
the teleſcope he made ufe of was fufpended in a vertical pofition by two 28
fmall cylinders fixt near the upper end of the tube, in fuch a manner that
the axis of each cylinder produced would be perpendicular to the axis of
the tube, and paſs through the fame: if the teleſcope were pulled a little
afide,.
638
BOOK 4.
ASTRONOMY
FIG. afide, the axis thereof, or the line of collimation, would fwing in the plane
of the meridian: from one of the cylinders hung a ſmall filver wire with
a plummet, reaching beyond the lower end of the tube, and immerfed in a
veffel of water to keep it fteady: the wire played freely upon a ſmall braſs
fector curiouſly divided by ſmall lines, diſtant 5 minutes from one another,
to be viewed by a microſcope: at every obfervation, the wire was firſt
brought to the point which it covered when it hung exactly perpendicular,
and there was fixed near the teleſcope a braſs plate with an hole and ſcrew,
on one end of which there was an index to be turned round within a circle
divided into an equal number of parts; the other end of the ſcrew was
pointed againſt the north fide of the tube; the threads of the fcrew were made
fo exact, that when it was turned round, the index would fhew how many
feconds the other end of the fcrew puſhed the axis of the teleſcope out
28 of the perpendicular: as I deſcribe all this by memory, I ſhall, in fig. 28,
give a view of a like inftrument, from Smith's optics, vol. 2. page 455.
Dr. Bradley affured me that he could depend upon being exact in his obſer-
vations by this inftrument, ſo as not to err above half a ſecond. When
he obferved he lay down upon his back on a cuſhion a little raiſed for the
head, which I found very practicable, for I made the experiment myſelf,
though there was nothing then for me to fee befides the croſs hairs of the
teleſcope, it being in the day time. One thing the Doctor told me which
may be of uſe to any one who would make the like obfervations, that he
put upon the upper end of the teleſcope, an hollow cylinder of paper or
paſteboard, of about a foot in length, to catch the dew, which would
otherwife fall upon the object glafs, and render it obfcure.
1476 The Newtonian philoſophy, after fome oppofition given at its firſt
appearance by the difciples of Ariftotle and Cartes, is now and hath been fome
years almoſt univerſally received in Europe, ſo that many able mathemati-
cians have employed their thoughts in confidering the various effects arifing
from the mutual gravitation of matter; and particularly in calculating the
force wherewith the heavenly bodies act upon one another. It was matter of
diſpute formerly whether the orbits of the planets continue invariable or not,
fee § 794: whereas, from their mutual attraction it is reaſonably concluded
a priori, that this is not the cafe; but that, how ſmall foever the alteration
in fome may be found by obfervation, they all fuffer a change in the places
of their aphelions and of their nodes. The fun being in the center of every
planets orbit, has a rotation round its own axis, the equator of the fun car-
ried to the heaven marks the via regia of the planets, wherein Kepler ima-
gined ſome emanation from that luminary had a tendency to carry all of
them
CHAP. 6.
639
ASTRONOMY
them round; but the reaſon affigned by him why they deviated every one
of them from that circle was fome particular repulfive faculty refiding in
each planet, which threw it out of the way wherein it would otherwiſe have
gone: this notion is fo unintelligible, as not to deferve an attempt to explain
or confute it. What may reaſonably be concluded from theory is, that every
planet hath a tendency to draw every other planet out of its orbit: when one
planet diſturbs the motion of another, the force of the diſturbing planet
depends upon the quantity of matter, diſtance, and direction of its motion:
it depends alſo upon the velocity of the planet diſturbed, becauſe the greater
the momentum is, the ftronger is the projectile motion, and the more
powerfully does it refift any attempt to change the direction thereof.
M. De la Lande has a curious paper, publiſhed among the Memoires of
the Royal Academy of Sciences at Paris for the year 1758, in which he
calculates from the data here mentioned what effect each planet hath to
cauſe a change in the places of the nodes of the orbits of every other
planet. As my preſent ſubject requires no more, I ſhall only ſet down
the reſult of his calculations; which is, that the interfection of the ecliptic
[Saturn 0,378
Saturn
Jupiter
will be changed
|
Jupiter
6,924
with the orbit of Mars
annually by the
Mars 0,094
Venus
attraction of
Venus 5,147
MercuryJ
Mercury 0,047
In the fame memoire it is fhewn that the obliquity of the ecliptic is di-
miniſhing at the rate of 47″ in 100 years by this action of the planets
diſturbing the plane of the ecliptic; and that the longitudes and latitudes
of the ſtars are affected by it. Calculations to this effect were first pub-
liſhed by Mr. Euler in the Memoires of the Royal Academy of Sciences at
Berlin for the year 1754.
1477 By Bradley's obfervations, it appears that the annual preceſſion of
the equinoxes is fometimes a few ſeconds more, fometimes lefs than the
mean preceffion of 50": this variation is owing to the different attraction of
the moon. The fame difference of the moons attraction which cauſes the
nutation of the axis of the earth, makes an equal variation in the fituation
of the terreſtrial equator, fo as to alter the angle between the plane of that
circle and the plane of the ecliptic, or change the obliquity of the ecliptic.
1478 The obliquity of the ecliptic may be changed two ways, one by
the equator changing its fituation as mentioned in the article immediately
preceding; the other by a real change in the orbit of the earth, cauſed by
the attraction of the other planets, or by the near approach of comets.
CHAP.
640
BOOK 4.
ASTRONOMY
CHAP. VII. THE SYSTEMS OF PTOLEMY, TYCHO Brahe, &c.
1479 What is commonly called the ſyſtem of Ptolemy, has its appellation
from that author, the oldeſt we have who has entered into the detail of it,
fo as to explain thereby the apparent motions of the fun, moon and planets:
this is fuppoſed to have been the oldeſt ſyſtem, and was received by the
ancient Greeks: fome few, however, of the difciples of Pythagoras held that,
the earth was carried round the fun as the planets are: against thofe Ariftotle
wrote, ufing ſeveral arguments to prove the earth to be at reft, de calo
1. 2. c. 13 & 14. The authority of this philofopher was thought to be of
fuch weight to eſtabliſh the old opinion, that it was generally approved till
Copernicus wrote his revolutiones orbium cæleftium; which, after fuppreffing
his book for fome years, in dread of the clamour he apprehended would be
raiſed againſt him, he was with difficulty prevailed upon to publiſh.
1480 In the Ptolemaic ſyſtem the earth is placed in the center of the
univerfe: round the earth the heavenly bodies are ranged in the following
order; neareſt to the earth, the orbit of the moon; next to that, the orbit of
mercury; then farther off, that of venus; then, that of the fun; then, thoſe
of mars, jupiter, and faturn: beyond all theſe the heaven of the fixt ſtars.
Some philofophers thought each of the ſeven planets, among which they
reckoned the fun and moon, were each of them fixed in a folid orb or
ſphere, and round the outermoft the fixt ſtars, placed in what they called
the eighth ſphere. To explain how all appeared every 24 hours to go
round us, they fuppofed a ninth ſphere, which they called the primum
mobile, or the firſt moveable. To this they attributed a whirling motion
from east to weft, impreffed thereon by the first mover or Supreme Being;
and that, this impreffion communicated itſelf to all the orbits below it,
and cauſed the apparent diurnal motion of the ſtars and planets: now, be-
cauſe they obſerved that the planets, while they were carried all one way
by the primum mobile, had each of them a flow motion the contrary way,
but with ſome obliquity, fo as to go through the zodiac in different pe-
riods; the moon in one month, mercury in about three months, venus in
about ſeven months, the fun in one year, mars in two years, jupiter in
twelve years, faturn in thirty years: they affigned to each planet an in-
telligence, which would turn its orb round in its proper period, while at
the fame time they were all fubject to the general motion. This is il-
luſtrated by a wheel being turned round, whilſt a fly creeps upon it the
contrary way.
The
+
Page 641.
.
#
32
BOOK IV.
H
G
B
D
T
31
}
C
A
B
M
H
15
E
33 G
N
с
}
97
CHAP. 7.
641
ASTRONOMY
The difference of the periodical times of the planets was probably the FIG.
reaſon why they placed their orbits in the order above defcribed; for, fince
they were certain from eclipſes, that the moon whoſe period is much ſhorter
than that of the fun, is alfo much nearer to us; they formed a general
conclufion that thoſe planets which perform their revolutions in the ſhorteſt
time are carried neareſt to the earth: this fyftem is reprefented by fig. 29, 29
wherein each circle is marked with the character of the planet to which it
belongs; the outermoft circle is that of the primum mobile, next under this
is the ſphere of the fixt ftars: fome place below the moon a ſphere of fire;
for which I find no other reafon given but this, that flame afcends, as
having a tendency to go to its proper place.
1481 Some philofophers imagined the planets to be carried in folid orbs,
which were ſo many ſpheres of chriſtal encloſed in each other, as the ſeveral
coats of an onion are: others held that each planet kept its circular way
fluid ether, a medium of very little or no refiftance.
in a
way in
1482 When the motions of the planets came to be obſerved with any
accuracy, the ſyſtem above mentioned could not account for their being
accelerated or retarded, direct, retrograde, or ftationary, their appearing
larger or leſs, confequently nearer to us or farther off; and therefore aftrono-
mers invented theories as they called them.
1483 Theſe theories were excentrics and epicycles: it was fancied that a circle
is the moſt perfect figure, and was therefore the moſt proper for the heavenly
bodies to move in. To account for fome appearances of the planets, they
ſuppoſed them to move in circles the centers whereof were different from
the center of the earth; they added alfo an epicycle, a fmall circle which had
its center fixed upon the circumference of the excentric, called circulus
deferens, or the carrying circle: thus, fig. 31, let the place of the earth be T, 31
the carrying circle ABCD, whereon the center of the epicycle is fixed and
carried round according to the order of the letters; at the fame time the
planet, being fixed at a in the epicycle, goes round therein according to the
order of the letters abcd; now while the planet is going from d to a, viewed
in the ſphere of the heaven, by a ſpectator at T, its motion will appear to
be accelerated from F to G: it is ſwifteft in its direct motion, and ſmalleſt
becauſe fartheft from us at a: it is retarded from a to b, there, while the
viſual ray is a tangent to the epicycle, or nearly fo, it appears ftationary
at н: from b to c it is retrograde, and accelerated: it is ſwifteft in retrograde
motion, largeſt and brighteſt, becauſe neareſt to us at c, and appears at G:
from c to d it is retarded, ſtill retrograde, ſeems ſmaller and leſs bright, as
going from us, is again ftationary at d, and appears at r.
4 N
As
642
BOOK 4.
ASTRONOMY
FIG.
33
As the times of being direct, ftationary, retrograde, are of different lengths
in different planets, this was accounted for by afligning different proportions
between the epicycles and the carrying circles, as to the length of their
diameters, and the velocity of their motions.
In fig. 33, the carrying circle I m is an excentric, the center of which is
H, the center of the earth is G, the excentricity is GH: the broad white
circle is taken of a breadth equal to AD the diameter of the epicycle: by
fuch a figure as this was explained the variations in the diftance of a
planet from the earth: for, when its place was A, its diftance was the
greateft poffible: when at L, its diftance from G was the leaft that it ever
could be. In other fituations of the epicycle, and the planet moving
therein, the diſtance thereof from the earth was intermediate, between the
greateſt and the leaft. This figure is taken from Clavius upon Sacro Bofco,
p. 233, if any one thinks it worth while to fee a farther explanation thereof.
puts me in mind of an expreffion of Milton, who ſpeaks of the heavens,
as repreſented by this hypothefis, par. loſt b. 8. v. 80 &c.
It
To fave appearances, how gird the ſphere
With centric and excentric fcribbled o'er,
Cycles and epicycles, orb in orb.
Thus much I think fufficient to fay of the Ptolemaic fyftem; which is
now fo univerfally exploded, that I ſhould have taken no notice of it, if I
had not promiſed to explain it in my propoſals.
1484 The Egyptians, obferving that venus never was at a greater diſtance
from the fun than 48 degrees, and mercury not more than 28 degrees; and
that they were brighteſt when retrograde; held that theſe two inferior planets
did not revolve round the earth as a center, but attended the fun, and were
carried round in epicycles placed upon his orbit: for the reft they held the
moſt ancient fyftem; which, with this correction was embraced by many
of the ancients, as Cicero, Martianus Capella, &c. This is exhibited in
32 the 32 figure.
1485 Tycho Brahe, having in the year 1582, carefully obſerved mars in
oppofition to the fun, judged that planet to be nearer to the earth than the
fun was; this could not be reconciled with the ſyſtem of Ptolemy. Tycho,
though he diſcovered that comets are above the moon, did not find that their
apparent motion was affected by the annual motion of the earth; he had
not opportunities of making a fufficient number of obfervations for that pur-
poſe: it was afterwards diſcovered in the comet of 1680 by Sir Isaac Newton.
Tycho
CHAP. 8.
643
ASTRONOMY
Tycho fancied the earth too grofs a body to be capable of the motions FIG.
attributed to it by Copernicus: from which, but chiefly from miftaken notions
of fome paffages in fcripture about the ftability of the earth, he was induced
to invent an hypothefis different from the other two: there is a reprefentation
of it in the 30 figure; the earth is ſuppoſed to be at reft in the center; in a 30
fmall circle near the earth the moon is fuppofed to be carried round accord-
ing to the order of the figns in one month: at a greater diſtance from the
earth is the orbit of the fun, wherein that luminary goes round according
to the order of the figns in twelve months; and, being in the center of them
all, carries the orbits of the five planets along with him in his annual courſe,
while each planet goes round its own orbit, in its proper period: moreover,
he ſuppoſed with Ptolemy, the diurnal motion of the fixt ftars, and of the fun,
moon, and planets, to be owing to the impreffion of the primum mobile.
As to the immenfe rapidity of the motion of the ſtarry heaven here
fuppofed, Tycho answered that objection, by affuming a much leſs diſtance
of the ftars from the earth than hath been demonftrated, § 888. His
diſciple Longomontanus, a little mended the ſyſtem, by allowing the earths
rotation round its own axis. Other emendations of the fyftem are not
worth confidering.
1486 Some aftronomers, both ancient and modern, imagined the orbits of
the planets, among which they reckoned the fun and moon, to be each of
them carried round by an intelligence or fpirit, directing the motion thereof:
Kepler appears to have been of this opinion, by what he writes in his book
de ftella martis. This fuppofition feems to derogate from the wiſdom and
power of the fupreme Being, as if he who created them all, were not able
to fuperintend his own works.
1487 To the places in fcripture which ſeem to affert the ſtability of the
earth, and attribute the diurnal motion to the fun; the anſwer is, that the
fcripture being defigned for the general uſe of mankind to whom it is made
known, the facred writers did not intend to make men philofophers, or
mathematicians, but to inftruct them in piety and virtue, and direct them
in the way that leads to hapineſs in a future life; and therefore, that they
might be underſtood by all, they ſpeak of things as they appear to the vulgar:
thus they ſpeak of the heaven and the earth as if they were two principal
parts of the world, becauſe they feem fo to be; though mathematicians
know the earth to be but a point in compariſon to the ſtarry heaven: thus
the fun and moon are called the two greater lights; though it be known
to aſtronomers that the moon is much leſs than any of the ftars. In like
manner, to the end propoſed by the ſcripture it is of no confequnce whether
4 N 2
the
644
ASTRONOMY
BOOK 4.
the fun or the earth move, and therefore it fpeaks of the earth as being at
reft, and of the fun as being in motion, rifing and fetting, becauſe thoſe
bodies fo appear to us: the fun appears to rife and fet, and the earth appears
to be at reft. The fcripture, in order to be intelligible, condefcends to uſe the
common langauge: where it is faid one generation paffeth away but the earth
abideth for ever; the meaning is, that the earth continues the fame, notwith-
ſtanding the changes that are made in the creatures that move thereon.
CHAP. 8. OF A PLURALITY OF WORLDS.
1488 That the earth and all the creatures thereon were created to be
fubfervient to the ufe of man, we may believe upon the authority of the fa-
cred writer, pſalm 8: but, that the ſtars and planets were formed only to
befpangle the canopy of heaven with their glimmering, which does not
furniſh us with a twentieth part of the light the moon gives; I think, is not
at all probable: this is contrary to the obſervation made by the beſt phi-
lofophers, that nature is magnificent in all her defigns, but frugal in the
execution of them: it is commonly faid that nature does nothing in vain:
now by nature, in a found ſenſe, muſt be underſtood the prefent order and
difpofition of things, according to the will of the fupreme Being.
1489 The notion of a plurality of worlds was mentioned and explained
§ 625, with an intention to reſume the ſubject, after the planets of our ſolar
fyſtem had been more particularly confidered. That this doctrine was em-
braced by feveral of the ancient Greek philofophers we are affured by Plutarch,
Stobaus, and Diogenes Laertius; from which authors, Gregory hath given us
extracts, in the preface to his aftronomy: among the moderns, Hugens has
written a treatiſe, which he calls cofmotheoros, or a view of the world, worth
perufing; one thing however I muſt find fault with; that, in peopling the
planets with reafonable creatures, he infifts upon their being in all points
exactly fimilar to the human race, as to the ſhape of their bodies, and the
endowments of their minds: this is too confined a thought; for we cannot
but acknowledge that infinite power and wiſdom is able to form rational
beings of various kinds, not only in ſhape and figure different from the human,
but endowed alfo with faculties and fenfes very different; fuch as, in our
preſent ftate, we can have no idea of. Mr. Fontinelle in his pluralite des
mondes, an ingenious treatiſe, which, as well as that of Hugens, is tranf
lated into Engliſh, handles this ſubject in a very entertaining manner, in
a dialogue between an aftronomer and a lady of quality; and has fome
very
CHAP. 8.
645
ASTRONOMY
very good philofophical remarks: only inſtead of the tourbillons, or whirl-
pools of Cartes, which was then, in France, the philofophy in vogue, we
muſt ſubſtitute ſtarry ſyſtems, v. § 625.
1490 By what we have ſeen of the diſtances of the planets from the fun,
§ 917, it appears, that on venus the heat is more than double; and on
mercury more than ten times as great as on our earth; enough to make our
feas and lakes more than boiling hot, fo as to evaporate all into fteam: on the
other hand, if the diftance only be confidered, in jupiter, and much more
in faturn, the heat of the fun is fo diminiſhed, and the cold there fo
intenſe, that all liquids muſt be hardened into ice, and an entire ftop muſt
be put to all life and vegetation: but thefe objections will be of no force,
if we confider that the foil of the feveral planets, may be fuch, as to mode-
rate the exceffive heat, which would be occafioned by their too great nearness
to the fun.
May not the globes of mercury and venus contain mines of faltpeter,
which may cool their furfaces, and the air furrounding them, ſo as to render
them very convenient for the habitation of animals, and vegetation of plants?
We are told by Fontinelle, that there are ſome places in China, which by
their fituation would be very hot, but by reaſon of mines of nitre are ſo cold
as to have their rivers frozen.
On the other hand, may there not be in the globes of jupiter and faturn
fubterraneous fires, which may compenfate their diſtance from the fun, and
make them fit for the abode of animals, and the production of plants?
rays
1491 The ancients imagined the torrid zone of our earth, where the
of the fun fall perpendicular, was too hot to be habitable: whereas, it is now
known, that fome of the fineſt countries in the world are fituated therein; and
that the rainy ſeaſons cool the air in places, where otherwiſe the heat would
be infupportable. In fhort, we are fure that if the all wife fupreme Being
hath placed animals on the planets, he has fitted the inhabitants to the places,
and the places to the inhabitants.
1492 The ancients in the firft place confidered the moon as likely to be
inhabited. Aftronomers now tell us the moon has no atmoſphere, or ſo
thin an air as not to be fit for refpiration, fee § 1056, 1057. Fontinelle,
imagined that, as one day there is equal in length to about thirty of ours;.
the fynodical month being near thirty days, § 958. during half of this.
period, a place on the moon is illuminated by the fun; in the other half it
receives no light from him: the heat; continuing fo long as fifteen days.
without intermiffion, would force the inhabitants, if any there, to retire
into ſome of thoſe caverns, which the teleſcope diſcovers in the moon.
1493
646
BOOK 4.
ASTRONOMY
1493 Some authors have expatiated upon the feveral planets, and ſhewn
us what kind of days and years their inhabitants have, if there be any
upon them.
In mars the day is nearly of the fame length as upon our earth; the year
about two of our years.
In jupiter there is a perpetual equinox; the day is very near five hours
long; the rotation of jupiter being performed in nine hours fifty fix minutes,
§ 1172. the darknefs of the nights is alleviated by the faint light of one,
two, or three, and fometimes by all four of his moons; the year is there,
about twelve of ours.
As to faturn, the length of the day there is not known; his year is about
thirty of ours: his night, has not only five moons to diſpell total darkneſs
but his broad flat ring alfo illuminated by the fun, which for fifteen years,
fhews the bright fide to one half of the planet; and for the other fifteen
years, turns the dark fide to the fame part of the planet, § 1135. v. Greg.
Íib. 6. prop. 6.
We cannot tell whether mercury has the diverfity of day and night, or
not, but can only conjecture from analogy, it being probable he has a rota-
tion, like the reſt of the planets: his year is about three of our months.
Venus has a moon attending her, § 948, 1367: as to her days and nights
they are nearly the length of our own, according to Caffini; though Bianchini
makes them much longer, § 1181: her year is about feven of our months:
the pofition of her axis muſt make a very great difference in the feafons
of her year, § 1183.
But theſe ſpeculations ſhould not take up too much of our time and
thoughts: the angel Raphael in Milton, book 8. gives Adam advice, which
the wiſeſt of his fons would do well to follow.
Sollicit not thy thoughts with matters hid:
Leave them to God above, him ferve and fear:
Of other creatures, as him pleaſes beſt,
Wherever plac'd, let him difpofe: joy thou
In what he gives to thee.
Be lowly wife:
Think only what concerns thee and thy being;
Dream not of other worlds; what creatures there
Live, in what ſtate, condition, or degree.
blak
HISTORY OF ASTRONOMY. BOOK V.
CHAP. I. INTRODUCTION TO THE HISTORY.
1494 I place the hiſtory of aſtronomy at the end of this work, becauſe in
relating when, and by whom any diſcovery in that ſcience was made, it is
ſuppoſed that the reader is before acquainted with the thing ſaid to be
diſcovered: thus, when Anaximander is faid to have been the firſt among
the Greeks who determined the obliquity of the ecliptic, the meaning of
thoſe terms is fuppofed to be previously known.
1495 The hiſtory of aftronomy has been treated of by ſeveral authors, of
theſe a principal one is Job. Fred. Weidler, profeffor at Wirtemberg,
who, in the year 1747 publiſhed a volume in 4to of 624 pages. In his pre-
face he mentions Ricciolus, Voffius, Gaffendus, Caffini, and Bullialdus, who
had written before on the fame fubject; to which may be added Curtius
in his preface to Tycho's obfervations. In the courſe of the work he takes
notice of every perſon whom he had found in any author mentioned to have
cultivated the ſcience, in whatever part of the world he lived, from the moſt
remote antiquity to his own time: it is a learned work.
Weidler divides his book into 16 chapters: the 1ft chapter is about the
fabulous hiſtory of aftronomy; the ftories of Ouranus, Atlas, Hercules,
Prometheus, &c. chap. 2, the aftronomy of the patriarchs; Adam, Seth,.
Enoch, Abraham, Mofes, Job: chap. 3, of the Chaldeans and Phenicians:
chap. 4, of the ancient Egyptians: chap. 5, of the Greeks before the found-
ing the ſchool of Alexandria: chap. 6, from the Alexandrian ſchool to the
birth of Chriſt: chap. 7, of the eight firſt ages after Chrift: chap. 8, the
aftron-
648
BOOK 5.
ASTRONOMY
aftronomy of the Arabians: chap. 9, of the Perfians and Tartars: chap. 10,
of other orientals, the Moguls, Siamefe, Chineſe, Americans: chap. 11, of
the Jews: chap. 12, of the middle ages; namely, 9, 10, 11, 12, 13, 14,
centuries: chap. 13, the 15th century: chap. 14, the 16th century: chap.
15, the 17th century: chap. 16, the 18th century.
1496 The learned Mr. Coftard of Oxford, printed three letters to Martin
Folkes Efq; one in 1746, the other two in 1748, concerning the rife and
progrefs of aſtronomy amongſt the ancients: in 1767, the fame author pub-
liſhed the hiſtory of aftronomy in a 4to of 368 pages: in the introduction are
propofitions of trigonometry; in the body of the work he inferts many
problems relating to the ufe of the globes: he brings the history down to his
own time, and gives ſome account of Sir Ifaac Newton's diſcoveries: he treats
alſo of the creation, and the general deluge.
1497 R. Heathcote, A. B. of Jefus College, Cambridge, in 1747, publiſhed
the hiſtory of aftronomy, a ſmall 8vo in latin of 82 pages, an ingenious
performance: he divides it into two parts; the firſt treats of the rife and
progrefs of that fcience; the fecond, of the ancient methods of philofo-
phifing, with a ſhort account of that of Sir Ifaac Newton.
1498 In 1754 Mr. Eftéve, a member of the R. Academy at Montpellier,
publiſhed three ſmall volumes in 12mo; wherein, I think, he is too fevere in
blaming Weidler, for fancying he had compofed a compleat hiftory of aſtrono-
my, by copying at length paffages out of authors who had faid any thing
about it, and accufes him of want of judgment, and of relating ridiculous
and improbable ſtories. He allows that Caffini has fome good things in
his treatife, which he would make uſe of in his work; but at the fame time
finds great fault with his being often obfcure, and too concife. He pretends
to give us, what he thought was hitherto wanted, a work made upon a good
plan; wherein, he fays, we fhall have an account of the progrefs of the
human mind in the profecution of the ſtudy of aftronomy.
1499 That excellent aftronomer M. De la Caille, in his introduction to
his ephemerides des movements celeftes, printed 1763, has given an hiſtory of
aftronomy, written with candour: he declares, that he does not propoſe to
make an exact enumeration of all the new diſcoveries, or to give the exact
dates of them, or to affign the true authors of them, or even to mention thoſe
who have contributed to the perfecting what was before invented, but will
fet down only fuch as are inconteftable; that he does not even write opinions,
but fuppofes what he mentions to be already in the poffeffion of the publick,
and only brings together into one view the principal things, that it may appear
what
CHAP. 2.
649
ASTRONOMY
what an immenfe difference there is between the knowledge of ancient times
in aſtronomy and the diſcoveries made within theſe 30 years laſt paſt.
1500 M. De la Lande, well known in the learned world for his aftronomi-
cal labours, printed in 1764 his aftronomie in two large volumes in 4to, an
excellent performance, confifting of 12 books, whereof the ſecond book is en-
tirely upon the origin and hiſtory of aftronomy: he carries it on to the time
of his writing.
The firſt and laſt of theſe authors made fo diligent a fearch into ancient
and modern books, that I ſhall ſeldom have an opportunity of quoting any
thing that is not to be found in one of them.
CHAP. 2. ASTRONOMY OF THE ANTIDILUVIANS.
1501 Aftronomy is a ſcience of great antiquity; ſome of the firſt principles
of it muſt have been known from the beginning of the world: the difference
between day and night, the rifing and fetting of the fun, the different hight
to which that luminary aſcends, in the ſame country on different days, the
various degrees of heat he communicates, the changes in the face of the moon,
and the returns of the fame; the great canopy of the heaven diverfified with
a prodigious number of ſtars of different magnitude, the diurnal motion of
the heavenly bodies, are ſtriking objects that muſt have drawn the attention
and excited the admiration of all reaſonable beings, who could fee and con-
fider: fome fingle ſtars, as firius, capella, aldebaran, and others of the firſt
magnitude, fome groupes of ſtars, as the great bear, orion, the pleiades, &c.
are fo remarkable, as to be eaſily diſtinguiſhed from the reft. Beſides the
fixt ſtars, the planets, by their different brightneſs and colour, but especially
by changing their places among the ſtars, muft foon have been taken
notice of.
1502 Adam at his firſt creation was not left bewildered in that aſtoniſh-
ment he muſt have been feized with, had he found no guide to inform him
how he came into a world fo full of wonders: it appears from the facred
hiſtory that he had frequent communications from the Divine Being: he is
faid to have been made after the likeneſs and image of God; from this
expreffion, fome have concluded he was created with the powers of his mind
in fuch perfection, as to have had the knowledge of the nature of all viſible
things, in a very high degree: one proof of this is, that he was able to give
names to the creatures brought before him for that purpoſe; names ex-
preffive of their outward form, or their inward qualities, as the learned
40
Bochart
650
BOOK 5--
ASTRONOMY
Bochart obferves, de animal. S. S. Some of the ancient Rabbins are ſaid to
have been of opinion that he knew the nature of the heavenly bodies, their
influence and uſes: but, what knowledge he or his firſt deſcendants had of
thefe matters, we can only conjecture; the fcripture is filent about it.
1503 Whatever knowledge our firft parents had of the heavenly bodies, this
we may be affured of, they had in their ſtate of innocence, enough to give
them a grateful fenfe of the beneficence of their creator, who had placed
them in fo happy a fituation, and had adorned their habitation with fuch
magnificence. It is therefore with great propriety that our incomparable
poet has reprefented them celebrating his praiſes, in a morning hymn,
part of which I fhall here tranfcribe, in hopes it may put many of my
readers in mind of thoſe ſentiments with which every man ought to look
up to heaven; the purpoſe for which an heathen poet thought man had
his erect ftature given him.
Pronaque cum fpectant animantia cetera terram,
Os homini fublime dedit cælumque tueri
Juffit, et erectos ad fydera tollere vultus.
Whereas the brutes all prone look down on earth,
To man an upright countenance was given, that he
Might raiſe his eyes to heaven, and view the ſtars.
The hymn of Adam and Eve from Milton's paradife loft, book
Theſe are thy glorious works, parent of good,
Almighty, thine this univerfal frame,
ADAM.
EVE.
ADAM.
EVE.
Thus wond'rous fair; thy felf how wond'rous then!
Unſpeakable, who fit'ſt above theſe heav'ns
To us invifible, or dimly feen
In theſe thy loweft works: yet theſe declare
Thy goodneſs beyond thought, and power divine.
Speak ye who beft can tell, ye fons of light,
Angels; for ye behold him, and with fongs
And choral fymphonies, day without night,
Circle his throne rejoicing: ye in heaven;
On earth join all ye creatures to extoll
Him firſt, him laſt, him midſt, and without end.
Faireſt of ſtars, laft in the train of night,
If better thou belong not to the dawn,
5.
Sure
{
CHAP. 2.
651
ASTRONOMY
ADAM.
Sure pledge of day, that crown'ft the fmiling morn
With thy bright circlet; praife him in thy ſphere
While day arifes, that fweet hour of prime.
Thou fun, of this great world both eye and foul,
Acknowledge him thy greater, found his praiſe
In thy eternal courfe; both when thou climb'ſt,
And when high noon haft gain'd, and when thou fall'ft.
EVE. Moon that now meet'ft the orient fun, now fly'ft,
With the fix'd ſtars, fix'd in their orb that flies,
And ye five other wand'ring fires that move
In myftic dance not without fong, refound
His praiſe, who out of darkneſs call'd up light.
I have here given fo much of the hymn as is aftronomical, and have
affigned to Adam and Eve different parts of the fame, in the manner done
by the late ingenious Mr. Galliard, who fet the whole to excellent muſick.
In the verſes following theſe, our first parents call upon various parts of
the creation, as the facred writer does in the 148th pſalm, to joyn them in
the praiſes of their maker.
1504 Jofephus in his first book of the antiquities of the Jews, c. 2. gives
the following account; that Seth and his defcendants were perfons of happy
tempers, and lived in peace, employing themſelves in the ſtudy of aftronomy,
and in other fearches after ufeful knowledge: that, in order to preferve the
knowledge they had acquired, and to convey it to pofterity, having heard
from Adam of the flood, and of the deftruction of the world by fire; they
made two pillars, the one of ftone, the other of brick, and infcribed their
knowledge upon them, fuppofing one or the other of them might remain
for the uſe of pofterity: the ftone pillar, fays he, on which is infcribed,
that there was another pillar of brick made alfo, is ftill remaining in the
land of Seriad unto this day. But this account is now generally rejected.
The learned Shuckford thought it a mifapplication of a paffage in the
Egyptian hiſtory, about ſome pillars faid to be infcribed by the first Mercury,
Thyoth. See his connect. vol. 1. pag. 45.
Jofephus, and Philo alfo, another Jewish writer, are thought to be partial
to their countrymen, attributing to them more ſkill in arts and fciences than
they really were maſters of: not confidering the far greater advantages they
enjoyed, in having the divine oracles committed to them.
1505 When the lives of men were eight or nine hundred years long,
as in the firſt ages of the world, genefis, c. 5. one man might obferve faturn,
40 2
the
652
ASTRONOMY
BOOK 5.
the floweft of the planets, go through more than twenty of his periods:
the antidiluvians therefore might ſome of them have been pretty good aftro-
nomers: and though, if they had any written accounts of aftronomical
obfervations, or any other inftructions in ufeful arts or fciences, the far
greatest part of them muſt have perished in the general deluge; it is not
probable that Noah a wife and good man, who was long before warned of
that great cataſtrophe, would neglect to fecure fome of the most valuable
of them with him in the ark.
Noah, is by fome learned men fuppofed not to have approved of the raſh
project of building the tower of Babel; but, fome time before the attempt to
put it in execution, to have retired towards the eaſt, with his poſtdiluvian
family; leaving Europe, Afia, and Africa to be peopled by Shem, Ham, and
Japhet; this, perhaps, will account for the Chineſe having fo early cultivated
the ſtudy of aftronomy, their being ſo well ſettled in an admirable police, and
continuing fo many hundred years as they did in the worſhip of the true God,
without any mixture of idolatry, till an execrable impoftor introduced
among them the worſhip of the idol Fo, the belief of a metempsychosis, or
tranfmigration of human fouls after death into the bodies of brute animals,
with the fuperftitions of the Bonzes. Du Halde, vol. 1. p. 367 edit. Paris fol.
1506 There is in fig. 78, book 1, an orthographic projection of the earth, I
copied it in a camera obfcura, from Senex's great terreftrial globe, the middle
thereof is Chaldea, a country not far from the place where the ark is ſuppoſed
to have reſted after the deluge; my intention in giving this print was to ſhew
how convenient this fituation of the ark was for the peopling, from thence,
Europe, Afia, and Africa.
As for America, we are not fure the earth and feas have continued in the
fame fituation as they were at the firft difperfion of mankind recorded in
genefis c. 11. Great continents may have been ſeparated by earthquakes,
large iſlands may have been fwallowed up in the ocean: an ancient tradi-
tion of fomething like this is mentioned by Platoa: large tracts of earth
may have been funk therein, fo as to leave only the mountains vifible;
which feems to be the cafe with fome cluſters of fmall islands, as the
Maldives, &c. and if no fuch change had happened, perfons going to fea
from the inhabited part of the earth, might by a ſtorm be driven to America,
or to ſome iſland in fight of fome part of that large continent.
1507 Jofephus, 1. 1. c. 3. fays God indulged the antidiluvians with a long
life, that they might bring aftronomy and geometry to perfection; that the
a In Timao, pag. 25. edit. Serrani.
firft
CHAP. 3.
653
ASTRONOMY
firſt of theſe could not be learned in leſs than 600 years; for that period, ſays
he, is the grand year, by which it is fuppofed he meant the period wherein
the fun and moon come again into the fame fituation as they were at the
beginning thereof, with regard to the nodes and apogee of the moon, &c.
this period, fays Caffini, whereof we find no intimation in any monument
' of any other nation, is the fineſt period that ever was invented; for it brings
out the folar year more exactly than that of Hipparchus and Ptolemy; and
'the lunar month within about one ſecond of what it is determined by mo-
*dern aftronomers. If the antidiluvians had fuch a period of 600 years, they
'muſt have known the motions of the fun and moon more exactly than they
were known fome ages after the flood'. Origine et progrès d'aftronomie, fol.
I cannot fee how fuch a period could be thought of, if the antidiluvians
had not diſcovered the fame by long obfervation; if ſo, we muſt reject the
opinion of Mr. Whiſton and his friend Mr. Allen, given § 1237, that before
the flood the year confifted of only 360 days.
'
Pliny 1. 2. c. 12, fays of Hipparchus, that he publiſhed an account of the
motions of the fun and moon for 600 years to come; this makes it proba-
ble that induſtrious aftronomer had the knowledge of the period in queſtion,
and gave an account of eclipfes for 600 future years: this could not be done
without tables, except they had fomething equivalent, as the Indian numbers
brought from Siam by Loubere, and explained by Dom. Caffini, in the regles
d'aftronomie Indienne pour calculer les mouvements du foleil et de la lune
expliquées. v. Recueil d'obſervations a Paris 1693.
CHAP. 3. ASTRONOMY OF FABULOUS TIMES.
1508 If we look into heathen authors, their oldeſt writers are the poets;
they, and fome of their hiftorians, mention Uranus as the most ancient aftro-
nomer: Uranus by Hefiod, is faid to be the ſon of Ge or the earth: may not
this be founded upon the true hiſtory of Adam being formed out of the
ground? We may find many ſcraps of the hiftory of the old teftament dif
guiſed in the fables of the ancients: v. Huetius demonftrat. and Stillingfleet's
origines facra.
The ſtory of Atlas fupporting the heaven, is thought to arife from his
having invented a ſphere: that of his brother Prometheus faid to be chained
upon Caucafus, and to have his liver preyed upon by a ravenous bird, might
be nothing more than a poetical image of an aftronomer wafting his fpirits, in
obferving the ſtars from that mountain: to name no more, when they talk
of
654
BOOK 5.
ASTRONOMY
of an amour between the moon and Endymion, they mean only to expreſs
the great affiduity with which that shepherd obferved the moon and the
feveral changes of her appearance.
CHAP. 4. ASTRONOMY OF THE CHALDEANS AND
EGYPTIANS.
1509 The Greeks are the moſt ancient writers of aftronomy now extant;
they do not pretend to be the inventors of that ſcience, but own they received
it from the Barbarians, as they called all thoſe who were not inhabitants of
Greece or the iſlands under the Grecian government, Plato in epinom.
Ariftoteles de cœlo.
The ſtory of the Rhodians carrying aftronomy into
Egypt, related by Diodorus Siculus, 1. 1. p. 32. is rejected by learned men.
1510 It was difputed between the Egyptians and the Chaldeans, which of
them firſt cultivated that ſtudy: the Chaldeans pretended, that Bel carried
aftronomy into Egypt: Bel fignifies Lord, probably the leader of the Chal-
deans from the difperfion had that title: he was deified after his death, as
many of the inventors of uſeful arts were, and was called Jupiter Belus.
Both Chaldeans and Egyptians pretended to an extravagant antiquity:
the Chaldeans vaunted their temple of Belus, built by Semiramis; their
Zoroastera, whom they placed 5000 years before the deſtruction of Troy: the
Egyptians oppoſed to them their colleges of priests, who ſtudied aftronomy
at Diofpolis, Heliopolis, and Memphis, the famous monument of Ofymandyas,
one of their kings; this Diodorus tells us was a golden circle (rather gilt I
fuppoſe) of 365 cubits round, one cubit thick. This circle the Perfians are
faid to have carryed away when Cambyfes invaded Egypt. The upper face
was divided into 365 parts, in every cubit was written the day of the year
and the rifing heliacally of the feveral ſtars for the day, together with the
prognoſtications from that rifing, according to their aftrology; I fuppofe the
meaning is as to the weather, to which the ancients paid great attention; as
appears by their calendars, wherein, after mentioning the rifing of fome
principal ſtars, we find naive in greek, or fignificat in latin; the meaning
whereof is, that it portends fome change of weather. v. Petav. uranol.
When Alexander took Babylon, Callifthenes enquired after the obſerva-
tions made by the Chaldeans; the moſt ancient that could be found were
no more than 1903 years before that time: this will carry them very near
to the time of the difperfion of mankind occafioned by the confuſion of
language..
a De Zoroastre, v. Huetii demonftrat. evangel. c. 5.
We
CHAP. 4.
655
ASTRONOMY
d
h
1511 We have now nothing left of the Chaldean aftronomy except fome
periods of
years, which they had formed for the more ready computing
of the motions of the heavenly bodies; yet, that they began to make
aſtronomical obfervations foon after this period is, I think, highly pro-
bable, if we confider the extent to which they had carried the ſcience of
aſtronomy, and the flow progrefs which they muſt have made in it, in
thoſe early times, for want of proper inftruments, and experience in ap-
plying fuch as they had. Yet notwithſtanding all theſe diſadvantages, if
we may believe Geminus, as quoted by Petavius in his Uranologion, they
had determined with tolerable exactneſs the length both of a periodical
and fynodical month, making the former to confift of 27 13 20′, and
the latter of 29° 12" 43′ 38″. They had, moreover, according to the fame
author, diſcovered that the motion of the moon was not uniform, and
had even attempted to affign thoſe parts of her orbit where it was greateſt
and leaſt. We are alfo affured by Ptolemy (Synt. 1. 4. c. 2.) that they
were not unacquainted with the motion of the moon's nodes, or that of
her apogee: they ſuppoſed that the former performed a complete revolu-
tion in 6585 days, or 18's 15d 8"; which period, containing 223 com-
plete lunations, is ufually called the Chaldean faros. And although, as
far as I can find, they did not attempt to affign the quantity of the laſt
mentioned motion, and differ fomewhat in the former three from what
later and more accurate obfervations fhew; yet, when we confider the
numberleſs diſadvantages they laboured under, we have great reaſon to
admire their affiduity and ſkill, and to lament that ſo very ſmall a por-
tion of their labours hath been handed down to us.
I know it has been fuppofed, that none of theſe obfervations were
made with any tolerable degree of accuracy, and that much the greater
part confifted only of the achronical, cofmical, and heliacal rifings and
fettings of the fixed ftars and planets: fome of them, however, we are
affured, were of more confequence, and deferved to have been preſerved
with more care than they have been. Ptolemy, from Hipparchus, gives us
ſeveral obfervations of lunar eclipſes which had been made at Babylon, the
oldeſt of them about 720 years before Christ; but we are not to conclude
from hence, that this induſtrious aftronomer could meet with none of a
more early date: the chronology of the Chaldeans was very imperfect be-
fore the æra of Nabonafar, which began 747 years before Chrift; it would
therefore have been very abfurd in Hipparchus to employ eclipfes which
had been obſerved before that period, in determining the motion of the
4 P
moon,
656
BOOK 5.
ASTRONOMY
moon, when the times of fuch eclipfes could not be afcertained on this
account.
We are moreover given to underſtand by Ariſtotle (de cœlo, b. 2.
c. 12.) that there were amongst them many obſervations of the occul-
tations of fixed ftars and planets by the moon: and from hence, by a
very natural and eafy inference, they were led to conclude, that eclipſes
of the fun were cauſed by the interpofition of the fame body; and the
rather, as they were well aware, from their knowledge of the moon's
motion, that this phenomenon always happened when ſhe was in the
fame part of the heavens in which the fun then was. The tower of Belus,
defcribed by Herodotus, as being furrounded with ſtairs on the outſide,
with landing places covered over, is thought to have been built for the
purpoſe of making aftronomical obfervations.
1512 The Chaldeans had moreover a confiderable ſhare in forming the
fixed ftars into conftellations, as is allowed by every one, and indeed as
appears from the names of feveral; but eſpecially thoſe which are men-
tioned in the book of Job, and other parts of the holy ſcriptures.
1513 Their faros, confifting of 223 lunations, as has been mentioned
above, is an undeniable inftance of their having made confiderable ad-
vances in the knowledge of the motions of the two luminaries. Geminus
calls this period eğeλeλyµos a revolution: Ptolemy, 1. 4. c. 2. αποκατάςασις
a reſtitution, and attributes it to the oi apxao, the ancients; by which word
he means the ancient Chaldeans, or Babylonians, before the conqueſt of
Babylon. The mean folar year of the Chaldeans, which refults from this
period, is 365 5" 49′ 30″, or 30" longer than de la Hire and Dom. Caffini
made it, and 33″ longer than Newton; but fhorter by 6" 25" than Hip-
parchus fuppofed it to be. See Halley Phil. Tranfa&t. for the year 1691,.
and Append. Aftronom. Carolin. Flamsteed præfat. hift. cœleftis.
d h
1514 Neither had comets, which have fo much perplexed the aftrono-
mers of later ages, eſcaped the notice of the Chaldeans; for we are told
both by Diodorus Siculus, and Apollonius Myndius in Seneca, that many of
them held comets to be lafting bodies, which have ſtated revolutions, as
the planets have; but in orbits vaftly more extenfive: on which account
they are feen only by us while they are near the earth; and diſappear by
going into other regions, at too great a diſtance to be vifible. He adds,
that from a long feries of obfervations, they were able to predict the ap-
pearance of theſe phenomena; but as they are alfo faid to have been able
to prognoſticate earthquakes and tempefts by the fame means, it is highly
probable,
1
CHAP. 4.
657
ASTRONOMY
probable, that their knowledge in theſe matters was rather the reſult of
meer aftrological predictions, than of any real aftronomical theory of the
celeſtial motions. Others of them, it is faid, were of opinion that comets
are only meteors, raiſed up into the air, which blaze for a time, until
the matter of which they conſiſt is confumed or diſperſed, and then they
diſappear. See § 1292.
1515 What has hitherto been faid of the Chaldeans is much to their
honour, as it fhews the great proficiency which they had made in the
knowledge of the nature, and the motions of the heavenly bodies; but it
is an eternal diſgrace to them, that they were fo fhamefully bigotted to
the vain and fenfelefs belief of, and fondnefs for, judicial aftrology, that
a Chaldean became a common name for any one, who made a profeffion of
foretelling future events by obſerving the poſition of the ſtars and planets.
1516 When I had proceeded thus far, a book fell into my hands in-
titled hiftoire des mathematiques, by M. Montucla of the R. Academy of
Pruffia, printed in two volumes, in 4, at Paris, in 1758; the learned
author, befides an hiſtory of the rife and progrefs of pure mathematics,
takes in aſtronomy alfo, and has many judicious reflections upon it: he
commends Weidler's work in general, as a laborious and uſeful collection,
but finds fault with the firſt chapters as a confufed heap of things: he
criticiſes Eſtéve feverely enough, as he deferves, for ſeveral groſs miſtakes:
he thinks the explications given § 1508 of Atlas fupporting the heavens,
of Prometheus his puniſhment, of Endymion's amour, puerile; and, paffing
over the fabulous hiftory, allows the Chaldeans or Babylonians and Egyp-
tians to be the moſt ancient cultivators of aſtronomy: this we are affured
of by Plato, Ariftotle and Cicero.
1517 An Arabian aftronomer, Albategnius de fcientia ftellarum, (c. 27.)
fays the Chaldeans and Egyptians made the fydereal year 365 6" 11'; the
naming of the fydereal year induces Montucla to think they had diſcovered
the preceffion of the equinoxes. Herodotus (1. 4.) tells us the Greeks
learned of the Babylonians to divide the day into 12 equal parts, and alſo
the uſe of two inftruments, the pole, and the gnomon: what the latter is
we know well enough; the pole was a moveable inftrument, for we find
one fixed in the famous fhip of Hieron, defcribed by Athenæus (1. 5.): it
feems to have been a ring-dial.
Dialling was known among the Babylonians 250 years before they had
any fuch thing among the Greeks; (for we read of the fun-dial of Abaz)
4 P 2
the
658
BOOK 5.
ASTRONOMY
the knowledge of which was owing to the intercourfe which the Jews had
with the Babylonians; it fhould feem that the going back of the fhadow
was obferved by the Babylonian aſtronomers; for we find the king of Ba-
bylon ſent an embaſſy to Hezekiah, to enquire about that miraculous ap-
pearance, 2 chron. ch. xxxii. ver. 31.
1518 The Egyptians appear to have been as early in their ſtudy of
aſtronomy as the Chaldeans; their country is flat, was peopled by Ham,
or his fon Menes: it is called in fcripture the land of Ham; from Menes,
or Miſor, it had alſo the name of Mifraim. That word in the dual num-
ber may have been uſed after its divifion into upper and lower Egypt.
They have to fhew, in their pyramids, the moſt ancient monuments in
the world of their ſkill in practical aſtronomy; for theſe are all fituated
fo that their ſeveral fronts face, very exactly, the four cardinal points
E. S. N. W. as Mr. Chazelles found them, in the year 1694. See Du
Hamel, bift. R. Acad. ann. 1696, et mem. R. Acad. 1710.
1519 Diogenes Laertius (1. 1.) tells us, they had in their annals ac-
counts of 373 eclipfes of the fun, and 832 of the moon, prior to the
time of Alexander the great; this is near enough to the ordinary propor-
tion between the number of eclipfes of the two luminaries, viſible in the
fame horizon; but their affigning for them 48863 years, is manifeftly a
vain fiction, calculated to raiſe the antiquity of their nation; for ſuch a
number of eclipfes might fall out in leſs than 12 or 14 hundred years.
1520 Simplicius, who lived in the reign of the emperor Juftinian, fays
that he had heard they had obfervations of the ſtars for 2000 years paſt;
that is, if he reckoned from his own time, about 1500 years before
Christ: what theſe obfervations were he does not relate; but it ſeems
highly probable that they were not particularly enough related to be uſe-
ful, as Hipparchus has made no uſe of them in determining the mean
motions of the fun and moon..
1521 Herodotus affigns their firſt knowledge of geometry, and aſtro-
nomy to Sefoftris, whom Sir John Marſham and Sir Ifaac Newton, with
other learned chronologers, take to be the fame with Sefac, mentioned
in the firſt book of kings, and therefore concludes that their knowledge
in theſe matters ought not be carried higher than about 1000 years be-
fore the Chriftian æra. But with due fubmiffion, it muſt be obſerved that
the Egyptians were famous for their learning at leaſt 500 years before that
time; fince we read. (acts c. 7. v. 22.) that Mofes was learned in all the
wiſdom
CHAP. 4.
659
ASTRONOMY
wiſdom of the Egyptians. What that wiſdom was, for which they were
then ſo noted, does not indeed appear with certainty, but that it was in
the ſcience of the ſtars is fcarcely to be doubted.
1522 Diogenes Laertius, from Manetho, fays that the Egyptians believed
the earth to be ſpherical, and that the moon was eclipfed by falling into
the earth's fhadow: the fame author alfo tells us, that they made their
obſervations with peculiar exactnefs; and that they could predict the
appearance of comets; but as he adds that they could likewife foretel
earthquakes, inundations, &c. it is to be prefumed that he knew but
little of the matter, and that little credit can be given to what he ſays in
this respect.
Macrobius affures us, that they had not only meaſured the magnitude
of the earth, but that of the fun alfo: he is particular enough in point-
ing out the method by which they did it; but it appears from thence,
that they made an affumption which is not true, and which led them
into a very erroneous conclufion.
1523 From the fame author we learn, that the fyftem of the world,
embraced by the ancient Egyptians, was, firſt ſaturn, then jupiter, within
him mars, next the fun with venus and mercury revolving round him, and
afterwards the moon, all revolving round the earth as a center. This dif
covery of mercury and venus revolving round the fun as a center, would do
credit to the ſkill of the Egyptians in aftronomy, could we be certain of
the truth of it; but Macrobius ſpeaks of it in ſuch a manner as renders it
probable, that he did not underſtand what he was ſpeaking of. Vitruvius
and Martianus Capella give a much more intelligible account of it, but
make no mention of the Egyptians. There are not, however, wanting
many who ſay that Pythagoras (who was the firſt among the Greeks that
taught that the morning and evening ſtar was the fame planet, which
ſometimes riſes before the fun in the morning, and at other times ſets
after him at night) learned this from the Egyptians: and ſome go even
farther, and affert that he was beholden to them for his whole fyſtem.
But it muſt be owned, that the Egyptian manner of naming the days of
the week from the planets, according to the Ptolemaic order, (§ 1231.)
diſcountenances this opinion; if this mode of naming them was not be--
gun by the later Egyptians, or rather the Greeks, when fettled at Alexan-
dria Dion Caffius hift. 1..37. p. 42. edit. Steph..
1524 The length of the year, both amongſt the Egyptians and moſt
other nations, confifted originally of 360 days, or 12 months of 30 days
each:.
660
BOOK 5.
ASTRONOMY
each: and from hence, no doubt, firſt aroſe the method of dividing the
ecliptic into 12 figns of 30 degrees each, and alſo circles in general into
360 degrees. But this length of the year was foon found to be too ſhort
for the return of the feafons; and on this account 5 days were added by
the Egyptians to the end of the year, making it thereby to confift of 365
days, but continuing, nevertheleſs, the nominal length of the year, as it
was before; and accounting theſe five days no part of it. This was firſt
done, as Syncellus informs us, about 1000 years after the flood, or 1348
years before Chrift; but Sir Ifaac Newton fuppofes it to have been done
much later: and it ſeems highly probable that this length of the year,
fo
corrected, was carried into, and was uſed throughout all Greece; and that
it was received from them, in the fame form by the Romans, and conti-
nued in ufe until the time when Julius Cæfar reformed the calendar, as
appears from Mr. Allen's learned differtation on this ſubject; and Sir Iſaac
Newton himſelf ſeems to be of the fame opinion. Chronolog. p. 81.
But befides the year mentioned above, the Egyptians made uſe of ano-
ther, uſually called the fothic year, from its beginning on the firſt day of
the month Thoth, or that on which Syrius, ufually called the dog-ftar,
rofe heliacally. It is generally fuppofed, that about the time of the foun-
dation of the Egyptian empire, the overflowing of the Nile was annually
announced by the heliacal rifing of this ſtar; and that it was for this rea-
ſon they made their year to begin at that time.
1525 As to the golden circle of Ofymandyas, Norden tells us, in his de-
fcriptions of the antiquities of Thebes in Egypt, p. 85. vol. i. and
P. 46.
vol. ii. that he had diſcovered the place where it was fituated, and that it
was near the palace of Memnon: Montucla treats the whole hiſtory of it as
a fable; but I cannot agree with him in this; becauſe the like might have
been faid of what we read in Herodotus concerning the pyramids, if they
had not been now ſtanding to vouch for the truth of his relation.
1526 But how famous foever the old Egyptians had been for their ſkill
in aftronomy, nothing remained of it in the time of Auguftus; for when
Strabo was there, they fhewed him indeed the large buildings where for-
merly the prieſts lived, and ftudied philofophy, [aftronomy] but he ſaw
no perſon who prefided over thofe affairs then; there were only ſuch as
attended the facrifices, and explained to ftrangers their religious rites and
ceremonies. They told him Plato and Eudoxus were 13 years in Egypt,
and ſhewed the apartments where they had ftudied with the priests.
น
1527 The
CHAP. 5.
661
ASTRONOMY
1527 The Egyptians were as much befotted in their fondneſs for judi-
cial aſtrology as the Chaldeans: the apotelefmata of Manetho, in Greek hexa-
meters, written in the time of Ptolemæus Philadelphus, and publiſhed by
Gronovius, are ftill extant; as well as fome treatiſes on that fubject, writ-
ten by Nicepfus, an Egyptian king, and Petofyris, a prieſt, which are ſaid
to be remaining in manuſcript in ſome libraries; it is pity they ſhould be
diſturbed, let them remain in their duft. To fay the truth, mankind
have every where, and at all times, manifefted fo great a defire of look-
ing into futurity, as eaſily to become the dupes of fuch as pretended to
foretell things to come.
CHAP. V. ASTRONOMY OF THE CHINESE, AND OTHER ORIENTALS.
1528 While we are ſpeaking of the claims which different nations have
made to an early knowledge in aftronomy, the Chineſe ought not to be
forgot, who boaſt themſelves to have cultivated that ſcience almoſt as
early as the flood. I take no notice of their vain and extravagant pre-
tenfions, prior to that event: but it ſeems to be generally allowed that
their firſt emperor Fobi was nearly contemporary with Noah, and he is by
ſome ſuppoſed to have been the fame perfon. Yao, therefore, the fixth
in fucceffion after him, might teach them aftronomy fo early as the
2300th year before the birth of Christ, which they affirm he did. They
farther affert, but improbably enough, that this emperor taught them to
fix the length of the folar year at 365 days and 6 hours nearly; and that
from him they received the method of dividing the heavens into 28 con-
ſtellations, and of finding the places of the fixed ſtars and planets in
them.
1529 Yao began his reign, as the annals of the Chineſe inform us,
about the year before Chriſt 2317. He is farther faid to have been the
inventor of their civil year, which is luni-folar, and begins from the in-
ſtant of that new-moon which happens neareſt to the time when the fun
enters the 15th degree of aquarius; (Du Halde, p. 90.) at which time a
feftival of tillage, as they call it, is folemnized; and they call that day the
beginning of fpring. It may not be improper to obferve here that the
Chineſe chronology extends back 2455 years from the birth of Chriſt to the
beginning of the reign of Fobi; which agrees well enough with ſcripture,
according
662
BOOK 5
ASTRONOMY
according to the Samaritan and Septuagint texts, though not with the
Hebrew. Magalhaens extends it only to 2357 years before Chriſt.
Some of the Jeſuit miflionaries have met with traditional accounts
amongſt the Chineſe of their firſt emperor Fobi having taught them aftro-
nomy; but in what this aftronomy confifted they have not been able to
find: however, Kempfer informs us (145) that he diſcovered the motions
of the heavens, divided time into years and months, and invented the
twelve figns into which their zodiac is divided, viz. 1. The mouſe, 2. the
ox, or cow, 3. the tyger, 4. the hare, 5. the dragon, 6. the ferpent, 7. the
horſe, 8. the ſheep, 9. the monkey, 10. the cock, or hen, 11. the dog,
12. the boar.
1530 The Chineſe have in uſe a period of 60 years which they ſay was
invented by Hang-Ti, one of their emperors, and grandfon to Fohi: they
fay likewiſe that he found out the pole-ſtar and the fea-compafs; alfo that
in his time a ſphere was invented, but of what kind is not known.
About 2800 years before the birth of Chriſt, the ftar a of draco was in
the folftitial colure, and therefore must have been about ten minutes
from the pole, and might be thought the pole-ſtar, and immoveable by
fhepherds, who are most likely to have been the obſervers.
α
1531 Chun, who fucceeded Yao 2277 years before the Chriftian æra,
finding a great quantity of gold and jewels in the palace, made a ſphere
which repreſented the feven planets, and employed therein precious ſtones
which beft correfponded to each: I fuppofe the meaning is, in colour or
fuppofed virtues.
1532 It is obferved above that they divide the heavens into 28 conſtel-
lations; they affign four of thefe conftellations to each of the ſeven
planets, ſo that the year begins always with the fame planet: they more-
over include in them all the ftars which are in the heavens, as well
thoſe which lie in the zodiac, as thofe which lie out of it. The names
of theſe conſtellations, according to Du Halde, vol. iii. p. 96. are,
1. Kao.
2. Kang.
8. Teou.
9. Lieou.
15. Juey.
16. Leou.
3. Ti.
Io. Niou.
22. King.
23. Quey.
4. Fang.
17. Guey.
11. Hio.
24. Licou.
18. Mao.
5. Sin.
12. Guey.
6. Vi.
19. Pie.
13. Che.
7. Ki.
20. Tſuy
14. Pie.
25. Sing.
26. Chang.
27. Ye.
21. Tfan.
28. Chin.
Thefe
CHAP. 5.
663
ASTRON
ASTRONOMY
•
Be-
Theſe anſwer not only to four complete revolutions of the planets, but
alſo to the twenty-eight manfions of the moon ufed by the Arabian aftro-
nomers. Theſe conſtellations, we are farther told, are not of equal
magnitude; that is, do not extend through equal portions of the ecliptic;
but, taken all together, make up a complete revolution through it.
fore I quit this fubject, it may be proper to obferve, that we meet with
ſome ſcattered imperfect hints amongſt the writings of the millionaries of
a diviſion of the zodiac into 24 figns by the Chineſe aſtronomers; but I
can find nothing particular concerning it: perhaps it means no more than
that they ſometimes reckoned by half figns. See Magalhaen's hift. China,
P. 335. Du Halde, vol. ii. p. 30. 8vo edit.
The Chineſe do not give to their conftellations a form correfponding
to the name, as the Greeks did: in many inftances it is not poffible, as
the greater part of the above recited names exprefs in the Chineſe lan-
guage the dignities or employments of magiftrates; though ſome are the
names of rivers, mountains, provinces, or towns of China; and a few
are the names of domeſtic furniture, or inftruments of huſbandry. On
the northern part of the ſphere, they place the king, the queen, the heir
apparent, the guards and courtiers; but theſe are reprefented by ſingle
ftars, and not by collections of them: their conftellations are formed by
connecting the ſtars by ſtraight lines; and I remember that the old Lord
Pembroke once fhewed me a thin Chineſe book in 4°, in which the con-
ſtellations were formed by putting a ſmall circle for each ſtar, and tying
them together by a ſhort ſtraight line. In this manner the great bear
would be repreſented by the figure following:
1533 Much has been faid concerning the fkill of the Chineſe in pre-
dicting eclipfes, and of their early attention to the obfervation of thefe
phenomena. Du Halde, vol. iii. p. 8o. affures us, that the circumftances
of no leſs than 36 eclipſes of the fun are recorded by Confucius himſelf;
out of which there are but two that are falſe and two doubtful: he pro-
bably means, which do not agree with modern tables. Confucius lived
about 551 years before Chrift. Magalha. hift. China. p. 65. A remark-
able eclipſe happened, according to their accounts, in the first year of the
4 Q
emperor
664
BOOK 5.
ASTRONOMY
b
emperor Tchong-Kang: and we are informed that the two imperial aftro-
nomers Hi and Ho were put to death, becauſe they had neglected to
foretel it, which it was their duty to have done. This eclipfe has been
brought to prove the truth of the fun's ftanding ftill, as recorded in the
book of Joshua, c. x. v. 12, 13.. The Jefuits make the first year of
Tchong-Kang correfpond to the year before Chrift 2155, which is near
600 years before the time of Joſhua: and they tell us that the eclipſe hap-
pened about noon on the first day of the ninth moon, which alſo was the
time of the autumnal equinox. The first day of the ninth Chineſe moon
fell that year on the 11th of October, on which day the fun was moſt
certainly eclipſed, and that confiderably, at fome places under the parallel
of Pekin in China; but it is as certain that, according to our tables,
which repreſent other eclipfes that happened 2500 years ago exceeding
well, no part of it could be visible in China; the true conjunction, by
the time at Pekin, being 57 minutes after one in the morning, and con-
fequently the eclipfe would be over before the fun rofe: but ſays the in-
genious gentleman who made this remark, if we ſuppoſe the fun and
moon to have ſtood ſtill for the ſpace of 12 hours, or a natural day, it
would bring the time of their true conjunction to about two in the after-
noon of the fame day, and the eclipſe muſt then have happened agreeably
enough to the Chineſe account of it. P. Gaubil affures us, that the rela-
tion of this eclipfe, together with the circumſtances which attended it, is
found in the Chineſe hiſtory called Chi-Kang: he adds, that the eclipſe
which happened in the 776th year before the Chriſtian æra is recorded in
the text of the fame hiſtory; from whence fome may infer that the former
is not in the text, and therefore may have been an interpolation. The
fame miſſionary affirms, that they knew the true length of the folar year
to be 365 days and a little leſs than fix hours at leaft 2000 years before
his time; that is, about 400 years before the birth of Chriſt. And P.
Trigault, who went to China in 1619, and who read more than 100 vo-
lumes of their annals, fays, "It is certain that the Chineſe began to
make aſtronomical obfervations foon after the deluge: that they have
obferved a great number of eclipfes, in which they have noted down
"the hour, day, month and year when they happened, but neither the
"duration or quantity; and that thofe eclipſes have been made uſe of in.
regulating their chronology."
b See Gent. Mag. for November 1758.
1534 But
CHAP. 5.
665
ASTRONOMY
1534 But out of this abundance it is much to be regretted, that ſo
very few of their obfervations have been particularized; for, befide what
has been mentioned above, we meet with no very ancient obfervations of
the Chineſe, except a winter folftice in the year before Chrift 1111, and
a fummer folſtice in the year 882 before Chriſt. Martini indeed ſpeaks
of a fummer folftice 2342 years before that æra; but M. Caffini, who cal-
culated it, found that there muſt have been an error in it of 500 years at
leaſt: an error of equal magnitude appears to have been committed in the
conjunction of the five planets, which it is pretended they obferved be-
tween the years 2513 and 2435 before Chriſt. See Loubere's account of
Siam, p. 257. Engliſh edit. 1693, and Renaudot's Differt. on this fubject,
p. 211. In ſhort, ſome have ſuppoſed that none of theſe are real obſer-
vations, but the refult of bungling calculations; and it has been hinted,
but furely on too flight a foundation, that even thoſe good fathers them-
felves were greatly to be ſuſpected.
1535 But however extraordinary theſe claims of the Chineſe to an early
knowledge in aſtronomy may appear, that, which they put in for, the in-
vention of the mariner's compafs is not lefs fo; for Du Halde affures us
(p. 330.) that above 1077 years before Chriſt, on the departure of am-
baffadors who had come from Core [Cochin China] the emperor prefented
them with an inftrument which had been made by the prime miniſter
Tahou-Kong, one end of which always pointed towards the north, and the
other towards the fouth, that they might find their way home better than
they had done from their own country to the court at Pekin. P. Gaubil's
account is much more modeft: he ſays, they were acquainted with the
directive power of the loadftone fo early as the year of Chriſt
225: and
that they were acquainted with the variation of the compaſs about 1101
A. C. Yet the Abbé Renaudot gives ſome reaſons for fuppofing that they
were not acquainted with either before they were introduced amongſt
them by Europeans. But let us come to things which are not conteſted.
1536 P. Gaubil acquaints us, that at leaſt 120 years before Chrift the
Chineſe had determined, by obfervation, the number and extent of their
conftellations, as they now ſtand; alfo the fituation of the fixed ſtars with
refpect to the equinoctial and folftitial points; as alfo the obliquity of the
ecliptic. He farther fays, that he cannot tell by what means it is that
they foretel eclipſes; but this is certain, that the theory by which they do
predict them was fettled about the fame time; and that they were ac-
quainted with the true length of the folar year, the method of obferving
4 Q2
meridian
666
BOOK 5.
ASTRONOMY
meridian altitudes of the fun by the fhadow of a gnomon, and of deduc-
ing from thence his declination, and the height of the pole long before.
We learn, moreover, from the fame miffionary, that there are yet re-
maining amongſt them ſome treatiſes of aftronomy, which were written
in the dynaſty of Han, or about 200 years before Chrift; from which it
appears that the Chineſe had known the daily motion of the fun and
moon, and the times of the revolutions of the planets for many years be-
fore that time.
1537 We learn from Du Halde, v. iii. p. 86. that in the province of
Ho-nan, and city Teng-fong, which is nearly in the middle of China, there
yet remains a tower, on the top of which, it is faid, Tcheou-cong, the moſt
skilful aſtronomer that China ever produced, made his obfervations.
This perfon lived about 1200 years before Ptolemy, or more than 1000
years before Chrift. He paffed whole nights in obferving the rifings, fet-
tings and motions of the heavenly bodies, and in forming their conftella-
tions. He uſed a very large braſs table, placed perfectly horizontal, on
which was fixed a long upright plate of the fame metal, both of which
were divided into degrees, &c. by which he marked the meridian alti-
tudes; and from thence derived the times of the folftices, which were
their principal epocha.
1538 The attention which the Chineſe formerly paid to theſe matters
induced them to erect a tribunal of aftronomy, the bufinefs of which is
to keep a meteorological journal, to predict the weather, as alſo droughts,
famines, and other like circumſtances; the accounts of which they are to
deliver in to the emperor every 45 days. Beſides theſe matters, it is the
buſineſs of this tribunal to calculate eclipfes of the fun and moon, and to
preſent to the emperor fome months before they happen, types of the
fame, with an account of the day and hour when, and of the part of the
heavens where they will happen; and how many digits the luminary will
be eclipfed. Thefe particulars they are to give in for the chief city of
every province, of which there are fifteen in China, in order that prepa-
ration may be made for obferving them.
1539 This tribunal is different from that called by the Chineſe Li-pou,
or the tribunal of rights, under which arts and fciences in general, and
the diſciples of Fo in particular, are placed. This fect, the peſt of China,
and by which it is now overrun, was introduced into that country about
the year of Chrift 64, according to Du Halde, v. i. p. 360. The empe-
ror, induced thereto by a dream, and a maxim of Confucius, which fays
1
that
CHAP. 5.
667
ASTRONOMY
that the Holy One would be found in the west, fent envoys into India, who
brought from thence Bonzes [fortune-tellers] who taught the doctrine of
metempſychofis, which they had learned from the impoftor Fo about 1040
years before.
1540 The preſent low ſtate of aftronomy in China has induced many
to fufpect the truth of theſe accounts, which are given of its former very
early fplendor; but perhaps too haftily. Thoſe who have attended to the
hiſtory of ancient times need not be reminded of the ſtrange and ſudden
revolutions which have ariſen from very trivial circumſtances in the affairs
of many nations befide the Chineſe. Two things, principally, feem to
have been the cauſe of this very extraordinary declenfion. In the firſt
place their emperor Thin-chi-hoang, about the middle of the third age be-
fore Chrift, ordered all their books to be burnt, except fuch as related to
agriculture and medicine; and in particular all books of obfervations, and
precepts of aftronomy were deftroyed, except fome few which had been
concealed, and which were carefully collected together after his death,
and preferved, rather as monuments of their former greatness in that
ſcience, than as materials, which might be uſeful to them in regaining it;
and which they ſeem totally to have defpaired of doing. We are no
where told what it was that produced this gothic decree: Mr. Coftard
thinks either that the aftrologers had foretold fome event of confequence
which never came to paſs, or ſomething which had a tendency to diſturb
the ſtate; in either of which cafes he thinks Thin-chi-hoang is to be juſti-
fied. But not to dwell upon this, which is foreign to my prefent pur-
pofe, we cannot be ſurprized that this unfortunate event, to call it no
worſe, caft an entire damp on the purfuits of aftronomy amongſt this
people, and that there were not, for a long time, amongſt them either
ſkilful aftronomers, or books of aftronomy; or even any known method
of performing thoſe things for which they had once been fo famous; or
that all which remained of their former labours were only confuſed tradi-
tions, catalogues of ſtars and conſtellations, and perhaps fome few frag-
ments of books which had lain long concealed. See Obferv. Aftron. par
Souciet.
Another circumſtance which, I think, contributed not a little to the
decline of aſtronomy amongſt the Chineſe was the introduction of the
bonzes foon after this general deſtruction of their ancient learning: for,
let authors diſguiſe it as they will, there is but too much reafon for be-
lieving that the principal motive amongst all the ancient nations, for cul-
tivating
668
BOOK 5.
ASTRONOMY
tivating aſtronomy, was the defire of prying into futurity; of which they
conceived it afforded them the means; and for which, after the introduc-
tion of theſe fortune-tellers, they had no farther occafion. To theſe, a
third reafon may be added for this decline, or at leaſt why a greater pro-
grefs has not fince been made in thoſe ſciences; which is, the great vene-
ration and reſpect that the Chineſe are taught to have for their anceſtors,
and their opinions, and which induces them to difcourage every thing
that brings not with it the fanction and approbation of former ages.
There can be no doubt but that they were very early maſters of the firſt
elements of fpeculative fcience; but this circumftance alone muſt have
prevented them from ever arriving at any very great degree of perfection.
It is faid, indeed, by the Jefuits, that learning is fo much encouraged
amongſt the Chineſe that no perfon can arrive at any of the great offices
of ſtate without it: but in what does their learning confift? It is princi-
pally in the knowledge of their characters, by means of which all their
other knowledge muſt be communicated; and this is a matter of no ſmall
difficulty: they have no letters to compofe words, as other nations have;
but one character ftands for a word, and fometimes for a whole fentence.
Of theſe characters they have a prodigious number: a man is thought to
have arrived at an extraordinary degree of learning who knows 80,000 of
them. The reſt of their ſtudies relate chiefly to their laws and their
morality.
1541 At preſent the moſt ancient catalogue of ſtars which the Chineſe
have was made in the year of Chrift 1050. Yuhi, who lived A. D. 284,
is the firſt of their aftronomers who mentions the proper motion of the
fixed ſtars, and he made it a degree in 50 years; nor was it until a cen-
tury after this time that they diſcovered the pole ſtar to have any motion:
before that time they thought it to be in the pole.
1542 There is a great conformity between the religion of China, Ja-
pan, &c. and that of Egypt, in worſhipping animals: their neighbours
in Afia worſhipped the fun, and the fire, becauſe it reſembles him. Hift.
Japan. p. 37. It is probable that they originally worſhipped the fun and
other luminaries of the firmament as parts of the creation, which moſt
ſtrike the ſenſes, and are moſt apt to fill the mind with admiration :
there are yet amongſt them ſome remains of the Chaldean worſhip of the
fun. Ibid. Kempfer makes it probable that in the year before Chriſt
536, when the ancient religion of the Egyptians was fubverted by Cam-
byfes, the prieſts, fleeing from thence, carried with them into the eaſt
fome
CHAP. 6.
669
ASTRONOMY
ſome of the Egyptian fuperftitions. Ibid. p. 38. perhaps fome of their
ſciences alſo.
1543 We are told by M. de la Loubere, embaffador from the French
king to the king of Siam in the year 1687, that the Siameſe had certain
aſtronomical rules, by which (without any kind of tables) they computed
the motions of the fun and moon, by divers periods of years and months,
and by the addition, fubtraction, multiplication and divifion of certain
numbers correfponding to theſe periods. The form of their year is luni-
folar, and they ſeem to have received this, with other arts and ſciences,
from the Chineſe; although they are not deſcended from them.
The Ja-
paneſe divide the natural day into 12 hours; from funrife to funſet ſix,
and fix from funfet to funrife: their 12 figns are the fame with thofe of
the Chineſe.
1544 The ſphere of the Indians, according to the Jefuits, is very dif-
ferent from any other, and confifts of the moft fimple figures, fuch as an
elephant's head and trunk, the goad they prick him forward with, an
umbrella, a fiſhing net, a trumpet, &c. The Indians divide the zodiac
into twenty-feven conftellations, and each conftellation into four parts,
each part being denoted by fome particular monofyllable. See Obferv.
Aftron. par Souciet. tom. i.
CHAP. VI. ASTRONOMY OF THE ANCIENT GREEKS BEFORE THE FOUNDA-
TION OF THE ALEXANDRIAN SCHOOL.
1545 We must not expect to find any thing, relative to aſtronomy,
amongſt the Greeks of like antiquity with what has been related of the
Chaldeans and Egyptians; but the lively imagination of that people, in
order to make a figure, prompted them to convert almoſt all their great
men into aftronomers: accordingly we find that there was ſcarcely a hero
amongſt them who is not dignified with a place amongſt the ſtars. Sir
Ifaac Newton refers moſt of the conſtellations to the time of the argonautic
expedition; but it is certain that fome of them were formed in much
earlier times: according to Apollodorus, Cepheus was an Ethiopian king,
Caffiopeia his queen, Andromeda their daughter, and Perfeus their ſon in
law. The ram and the bull were, probably, confidered under thoſe ap-
pellations long before the Greeks applied the former to the ſtory of
Phryxus and Helle, and the latter to that of Jupiter carrying off Io in the
ſhape
u
1
670
BOOK 5.
ASTRONOMY
ſhape of a bull. In ſhort, it is highly probable that ſhepherds and others,
employed in rural occupations, first gave names to fome of the more re-
markable ſtars, or groups of ftars; and that the poets afterwards invented
fables to fuit them, which Chiron might adopt when he formed the ſphere
of the Greeks. But whether Chiron firſt placed on the ſphere the conſtel-
lations now found thereon or not, it is certain that other nations had
figures very different from thefe; for the Egyptian, the Perfian, and the
Indian ſpheres were none of them the fame with the Greek ſphere, now
adopted by us. See Scalig. in Manil. p. 371. et 428.
a
Hefiod and Homer, the most ancient writers amongſt the Greeks, and
who, according to Sir Ifaac Newton, lived about 870 years before Chrift
both mention ſeveral of the conftellations. Hefiod, in particular, directs
the farmer to regulate the time of fowing and harveft by the rifing and
fetting of the pleiades; and tells us that arcturus rofe, in his time, as the
fun fet, 60 days after the winter folftice. Homer informs us that the
pleiades, orion, and arcturus were uſed in navigation. Theſe conſtellations
are generally thought, by learned men, to be the fame with thofe men-
tioned in the ancient book of Job by the names aiſh, chefil, and chimah;
and as they are fome of the moſt remarkable collections of ftars in the
heavens, we may conclude, with probability enough, that they were the
firſt taken notice of.
1546 Thales, the Milefian, was one of the most ancient, as well as the
moſt celebrated aftronomers of Greece; and is ſuppoſed to have been the
firſt who travelled into Egypt in ſearch of knowledge, and who brought
from thence the firſt principles of that ſcience, in which the Greeks after-
wards made fuch furprifing advances. The Egyptian prieſts were very
jealous of their knowledge, and exceedingly careful to conceal it from the
vulgar: Thales muſt therefore, without doubt, have been ſtrongly recom-
mended to them, before they would admit him, a ſtranger, to a partici-
pation of that knowledge which they fo induſtriouſly concealed even from
their own countrymen.
We are told by Diogenes Laertius that he determined the height of the
pyramids, when in Egypt, by meaſuring the lengths of their fhadows
when the fun was 45 degrees high, and when, of courſe, the lengths of
the ſhadows of objects are equal to their perpendicular heights.
a The learned and reverend Mr. Coftard has taken great pains to prove that the poets Hefiod and
Honer lived not more than 580 years before Chrift: the force of his arguments must be left to every
perfon's own judgement. I have adhered to former chronologers.
According
CHAP. 6.
671
ASTRONOMY
According to Sir Ifaac Newton, Thales began to flourish about the 41st
olympiad, or 615 years before the Chriftian æra. That the conjecture of
Sir Isaac, concerning the time when Thales lived, is nearly right, may be
gathered from the time of that famous eclipſe, predicted by him, which
happened juſt as the two armies under Alyattes, king of Lydia, and Cy-
axares, the Mede, were engaged; and being regarded by each party as an
evil omen, inclined both to make peace.
1547 The rev. Mr. Coftard and Dr. Stukely (Philof. Tranfact. vol. 48.
for 1753.) both conclude that this eclipſe fell out in the fourth year of
the 43d olympiad, or in the year before Chriſt 603, and according to the
latter of theſe gentlemen, on the 18th of May O. S. He fuppoſed that
the battle was fought near the city, now called Erzerum, over which the
ſhadow paffed at half an hour after eleven o'clock in the morning; and
the eclipfe was total there about 4 minutes.
The means by which Thales was enabled to predict this eclipſe is not
yet agreed on by polemical writers, to whom the determination of this
point has given much trouble: but perhaps the reader will not think it
any very difficult buſineſs, if he attends to what we have faid concerning
the knowledge, which the ancient Chaldeans and Egyptians had of the ce-
leſtial bodies, and the periods which they had framed of their revolutions
and motions; all which Thales, no doubt, had learned of the latter, during
his long ſtay amongſt them; and eſpecially, if he confiders further that
this prediction of Thales probably amounted to no more than that of our
illuftrious countryman Dr. Halley, concerning the late comet; viz. that it
would happen in fuch a year, without confining it farther either to time
or place, and which muſt have been matter of ſurpriſe enough to the
people of thoſe times.
548 Thales, according to Callimachus, formed the conftellation of the
leffer bear; or, at leaſt, introduced the knowledge of it into Greece. He
is moreover faid, by Diogenes Laertius, to have been the first who taught,
in that country, that the true length of the folar year was 365 days.
Pliny tells us that he determined the coſmical fetting of the pleiades to
have been 25 days after the autumnal equinox in his time. Plutarch
affures us, that he firft divided the earth into five zones by the polar
circles, and tropics; that he firſt ſpake of the obliquity of the ecliptic,
and fhewed that the equinoctial is cut at right angles by the meridians,
which all paſs through, and cut one another in, the poles. Stanley ſays
4 R
that
672
BOOK 5.
ASTRONOMY
that he held the fun's diameter to be one 720th part of his annual orbit;
which, if true, is a degree of precifion, much to be admired in the rude
knowledge of thefe early times. He is, moreover, faid by fome to have
obſerved the exact time of the folftices, and from thence to have deduced
the true length of the folar year; to have obferved eclipfes of the fun and
moon; and to have taught that the moon had no light of her own, but
that the borrowed it from the fun.
1549 Theſe things fhould, however, be received with caution: there
are ſome reaſons which might be affigned for fuppofing that the know-
ledge of Thales, in thefe matters, was more circumfcribed; and indeed it
is not unreaſonable to ſuppoſe that that veneration for the ancients, which
leads authors to write profeffedly on the hiſtory of ancient times, may
have induced them to afcribe full as much knowledge to thoſe who lived
in them as was really their due.
1550 Thales died, according to Diogenes Laertius, in the firft year of
the fifty-eighth olympiad, or 549 years before the birth of Chrift. He
was the founder of the Ionic ſchool, and his diſciples and followers, Anax-
imander, Anaxamenes, and Anaxagoras, who fucceeded him, all made fome
farther advances in aſtronomy.
1551 Anaximander, in particular, is faid to have invented, or intro-
duced the uſe of the gnomon into Greece, to have obſerved the obliquity
of the ecliptic; and taught that the earth was the center of the univerſe;
that it was ſpherical, and that the fun was not lefs than it. He is, more-
over, faid to have made the firft globe; and, by fome, to have ſet up a
fun-dial at Lacedemon, which is the firſt we hear of amongſt the Greeks:
the knowledge of which, together with that of the pole and gnomon,
fome think was brought from Babylon by Pherecydes, who was contempo-
rary with him; and who, about the fame time, according to Diogenes
Laertius, fet one up at the iſland of Syra, one of the Cyclades. This
Pherecydes, together with Thales, and many others of the ancient philofo-
phers, held that water is the firſt principle of all natural bodies: as this
doctrine cannot have been derived from any very obvious principles, fome
are of opinion that it was traditional, and has fome relation to the earth's
having been created originally in a fluid ſtate. Anaximander died in the
fecond year of the 58th olympiad, or the 547th year before Chriſt.
1552 Anaxagoras was the third in fucceffion from Thales in the Ionic
ſchool. He is faid to have predicted the eclipfe of the fun, which, ac-
cording
CHAP. 6.
673
ASTRONOMY
cording to Thucydides, happened in the first year of the Peloponnefian war;
and to have taught that the moon was habitable, as having plains, hills,
and waters, as our earth has.
1553 Contemporary with Anaxagoras was Pythagoras, the Samian, who
gave new light, not only to aftronomy and the mathematics, but to every
branch of philoſophy whatſoever. He was inftructed in the Greek learn-
ing in his youth, and afterwards travelled into Phoenicia and Egypt, be-
ing recommended to king Amafis by Polycrates, governor of Samos, and
by that means admitted to familiar converfation with the prieſts, and for
many years to a participation of the Egyptian learning. Some fay he was
taken captive there by Cambyfes, and by that means became acquainted
with all the divine myfteries of the Perfian Magi; being taught chiefly by
Zoroafter himſelf; and that having afterwards recovered his liberty, he fet
up a ſchool at Crotona, and became the head of the Italian fect.
$
Pythagoras taught that the univerſe was compofed of four elements;
that it was round, and had the fun in the middle of this mundane fyftem.
That the earth was round alſo like a globe, had antipodes, and that the
moon was enlightened by the rays of the fun. He held, moreover, that
the ſtars were worlds, containing earth, air, and ether; that the moon
was inhabited like our earth; and that the comets were a kind of wan-
dering ſtars, which diſappeared as they afcended towards the fuperior
parts of their circuit, but appeared again at their return, after long in-
tervals of time. He afcribed the brightneſs of the milky way to the effect
of a great number of ſmall ſtars, which are fituated in that part of the
heavens; and he fuppofed the diſtances of the moon and planets from the
earth to be in certain harmonic proportions to one another. He is far-
ther faid to have exhibited the oblique courfe of the fun in the ecliptic,
and the pofition of the tropical circles by means of an artificial fphere.
It was he alſo who firſt taught that the planet venus is both the evening
and the morning ftar, which fometimes rifes before, and at others fets
after the fun, as we learn from Pliny, Nat. Hift. b. i. c. 8. where he
writes thus, "Below the fun there is a beautiful ftar, called venus, who
performs her period, wandering fometimes this way, and fometimes that:
while fhe precedes the morning, and rifes before the fun, ſhe takes the
name of lucifer; on the other hand, when the fhines in the weft, pro-
longing, as it were, the day-light, ſhe is called vefper. Theſe particulars
relating to this ſtar were firſt found out by Pythagoras of Samos, about the
42nd olympiad."
4 R 2
1554 Philolaus
674
BOOK 5.
ASTRONOMY
1554 Philolaus of Crotona, is the next aftronomer of note that we meet
with: he flouriſhed about 440 years before Chriſt, and was one of the
moſt celebrated of the Pythagorean fect. He fhewed that the earth moved
in an orbit round the fun, according to the order of the ſigns; and ſoon
afterwards we find Hicetas, a Syracufan, afferting its diurnal motion
round its own axis.
1555 Much about the fame time with Hicetas lived Meton and Euctemon,
at Athens; according to Ptolemy, they obferved the fummer folftice in the
year when Apſeudes was archon; which was before Chrift 432 years, and
is the oldeſt obſervation of this kind that is come down to us, except what
we have from the Chineſe. Meton is alſo ſaid to have compofed a lunar
cycle of 19 years, which goes by his name: it contains 6940 days, and
has in it ſeven intercalary months; and he added to this cycle the motions
and fignifications of the ftars. Diodor. Vitruvius fays he marked the rif
ings and fettings of the ſtars, and what ſeaſons they pointed out: and in
all theſe matters Euctemon was his companion, and affifted him, as we
learn from Geminus and Pliny.
1556 Aſtronomy owes but little to the philofopers of the academic fect,
and yet leſs to the peripatetics. Plato, the founder of the former, is faid
by Theon, of Smyrna, to have been the inventor of epicycles; but let this
be as it may, it is very certain he embraced that ſyſtem, which is now
uſually aſcribed to Ptolemy; and Ariftotle, the founder of the latter ſect,
implicitly followed him in that reſpect. In other matters, relating to
aſtronomy, they contented themſelves with teaching what they had re-
ceived from thoſe who went before them. Plato was, nevertheleſs, a
great encourager of the mathematical ſciences, which he divided into
arithmetic, geometry, ſtereometry, mufic and aſtronomy; and is faid to
have cultivated the abſtract branches, arithmetic and geometry with great
affiduity. Ariftotle, poffeffed of a treaſure in practical aftronomy, which
was probably ineftimable, knew neither how to make uſe of it himſelf, or
fo much of its value as to induce him to uſe the neceffary means for its
preſervation to thoſe who might. How much is it to be lamented that
the Babylonic obfervations did not fall into the hands of his contemporary
Eudoxus, instead of his!
1557 Eudoxus, a Cnidian, was a ſcholar of Plato, and confequently,
as hath been faid above, contemporary with Ariftotle, though conſider-
ably older: he is called the prince of aftronomers by Cicero, de divinat.
ii. 42. and with fome reafon, for he was undoubtedly the firſt who ap
plied
CHAP. 6.
675
ASTRONOMY
plied geometry to the heavens. He flourished, according to Menagius.
Obferv. in vit. Eudoxi, p. 392. about 360 years before the birth of Chriſt.
In the earlier part of his life he travelled into Egypt, being recommended
to Nectanebo, king of Egypt, by Agefilaus, and by him to the prieſts, with
whom he converfed for a confiderable time, and learned from them many
things relating to aftronomy. After he returned from Egypt he taught
aſtronomy in Aſia, in Italy, and other parts; and had many ſcholars.
He particularly infifted on the neceffity of making aſtronomical obferva-
tions; and taught the manner of doing it. He corrected the Grecian
year, according to the precepts which he had received from the Egyptian
prieſts, adding, as Pliny informs us, fix hours to the folar year of 365
days. According to Seneca he firſt brought the motions of the five planets
(that is, the hypotheſis of their motions) out of Egypt into Greece.
Archimedes tells us that Eudoxus believed the fun's diameter to be nine
times as much as the moon's. Hipparchus, in his books upon Aratus,
often quotes Eudoxus with great praife for his knowledge in, and great
attention to aſtronomy. Vitruvius afcribes to him the invention of draw-
ing a fun-dial upon a plane; from whence it may be inferred that he was
tolerably well acquainted with the doctrine of the ſphere, and the method
of projecting its circles on a plane, which cannot be done without a con-
fiderable knowledge in geometry; and, indeed, there are many who think
that the greater part of what now bears the name of Euclid's elements of
geometry are his. But notwithſtanding what has been faid by many
authors, concerning the obſervations of Eudoxus, fome have queſtioned
whether his ſphere was not taken from one more ancient, as that of
Chiron, the centaur; becauſe, if the places of the ſtars had been taken
from obſervations made by himſelf, all the conſtellations would have been
farther advanced by half a fign than they are deſcribed to be in his writ--
ings. He is faid to have been a great enemy to judicial aſtrology.
1558 About the year 340 before Chriſt flouriſhed Calippus, of Cyzicus,
a city of the leffer Aſia: his ſyſtem of the celeſtial ſphere is mentioned by
Ariſtotle in his metaphyfics; but he is more remarkable on account of the
period of 76 years, which he is faid to have invented, and which goes
under his name, containing four corrected metonic periods, and which
had its beginning at the ſummer folftice in the year 330 before Chriſt.
1559 About this time, or rather earlier, the Greeks began to plant
colonies in Italy, at Marſeilles, and in Egypt; by which means they be-
came acquainted with the pythagorean fyftem, and the notions of the an-
cient.
676
BOOK 5.
ASTRONOMY
cient Druids concerning aftronomy. That the Druids were learned in
the motions of the ſtars is afferted by Julius Cæfar, who was firſt ac-
quainted with them: the fame author, Comment. 1. i. fays that the Gauls,
in general, were able failors; which, at that time, they could not be
efteemed without a competent knowledge in aftronomy: we are farther
confirmed in this opinion by what Cleomedes, 1. i. c. 7. relates of Pytheas,
who lived at Marfeilles about the time of Alexander the great, and ob-
ſerved the altitude of the fun there at the fummer folftice (§ 417.) by
means of a gnomon. Pytheas is alfo faid by Strabo to have travelled as
far as Thule to fettle the climates.
1560 From what has been related in the preceding chapters, it fully
appears that the Greeks can have no pretenfions to the invention of aftro-
nomy. The ſtory of the Rhodians carrying that fcience into Egypt, as
mentioned by Diodorus, is fo blended with fables as to deſtroy its own
credibility: the Rhodians were indeed fuperior to the reſt of the Greeks in
the art of navigation; but at that time navigation had little concern with
aftronomy. The period of 18 years, mentioned § 1511, was undoubt-
edly Chaldean; neither the Egyptians or Greeks having any common uſe
of it; or indeed of the period of 19 years attributed to Meton, or that of
76 years made uſe of by the firſt aftronomers; and it is highly probable
they were first brought into Greece from Chaldea by Berofus. The radix
of Ptolemy's calculation is manifeftly a Chaldean epocha, the beginning of
the reign of Nabonaſſar; and plainly from Berofus. It was fixed to the
26th day of February of an Egyptian year, 745 years before Chriſt, at
noon in Babylon; where Nabonaffar eſtabliſhed a new kingdom, that
country being, before his time, governed by a lord from Nineveh. The
Chaldean religion made it neceffary for prieſts to be aftronomers, for they
thought the ſtars to be the thrones of the divinities, who governed the
world under the direction of Bel, the fupreme lord.
Moreover moſt of the Greek writers, and Plato in particular, attribute
the firſt knowledge of aftronomy to the Egyptians and Chaldeans, under
which last name the Jews were generally comprehended. It is probable
the Patriarchs received the knowledge of what was fufficient for the uſe
of agriculture, and for diftinguiſhing ſeaſons by tradition from their firſt
parents. It is ſaid, Genefis i. that "God made the ſtars for figns and for
feaſons, and for days and years." Years and months were therefore
known before the deluge. In fhort, wherever there were men, there
muſt have been ſo much knowledge as to obferve the different ſeaſons of
the
CHAP. 7.
677
ASTRONOMY
the
year. They muſt have been fenfible that the fruits of the earth were
not to be gathered at all times of the year; fpring produces only the
flower, fummer forms the fruit, and autumn brings it to maturity, and
they are fit to be gathered. In the winter vegetables lie quiet in the
ground, and recover ſtrength to put forth in the ſpring; thus muft men,
in all places, have diſcovered, in fome degree, the length of the year; and
that the moon, by her variety of phaſes, marks out the length of the
month, is what a man muſt want eyes to be ignorant of. But, on the
other hand, it muſt be obſerved that the very pagans themfelves laugh at
the pretended antiquity of the Egyptians and Chaldeans: the obfervations
of 1900 years, fent from Babylon by Callisthenes to Ariftotle, carry theſe
matters (as hath been obſerved before) nearly up to the diſperſion of man-
kind; and from that time the firft rude beginnings of this fcience may
poffibly be dated.
CHAP. VII. ASTRONOMY OF THE GREEKS AFTER THE FOUNDATION OF
THE ALEXANDRIAN SCHOOL.
1561 After the death of Alexander the great, about the year before
Chriſt 324, his captains divided great part of the dominions which he
had conquered amongſt themſelves. Egypt fell to the ſhare of Ptolemy,
the ſon of Lagus, who made the city of Alexandria the capital of his
kingdom, about 305 years before Chrift.
before Chrift. His fon and fucceffor, Ptolemy
Philadelphus, a prince inſtructed in all kind of ſciences, and the patron of
thoſe who cultivated them, fet up a famous fchool there, unto which he
invited learned men, as well Greeks as others; and made fuch proviſion
for them as ſtirred up an emulation that laſted until the time of the inva-
fion, by the Saracens, in the year of Chriſt 650. It is from the time of
thefe Ptolemies that we may date the beginning of true aſtronomy.
1562 The first who cultivated aſtronomy at Alexandria were Timocharis
and Aryftillus, who began their obſervations on a new plan; inafmuch as
they were more exact in noting, and more particular in fetting down the
ſeveral times, when their obſervations were made. Ptolemy, in his alma-
geft, affures us that Hipparchus made uſe of their obſervations; by means
of which he diſcovered that the ſtars had a motion in longitude of about
a degree in one hundred years: he cites many of their obfervations, par-
ticularly thoſe of Timocharis, the oldeſt of which is in the reign of Ptolemy,
the
678
BOOK 5.
ASTRONOMY
the fon of Lagus, in the year before Chrift 295, when the moon, fays he,
juſt touched the northern ſtar in the forehead of the fcorpion; and the
laft of them in the 13th year of Philadelphus, the year before Chriſt 272,
when venus hid the former ftar of the four in the left wing of virgo.
1563 Aratus, much celebrated for a Greek poem called the Pheno-
mena, mentioned § 587, lived about 270 years before Chrift. Much
about the ſame time lived Ariftarchus of Samos, who was a ftrenuous
afferter of the Pythagorean fyftem of the world, as we learn from the
Arenarius of Archimedes: feveral aftronomical works are attributed to him,
and he appears to have been a perfon of the moft penetrating genius of
all the ancient aſtronomers. A moſt ſtriking inſtance of which he has
given in his method of determining the diſtance of the fun from the
earth by means of the moon's dichotomy. Ptolemy relates an obſervation
of a folſtice made by him, but does not affign the year when it was
made.
1564 Eratofthenes, born at Cyrene, 271 years before Chriſt, was a per-
fon ſkilled in all parts of learning, but particularly aftronomy and geogra-
phy. Very little remains of his works now befides his manner of deter-
mining the meaſure of a great circle of the earth by means of a gnomon.
His reputation for learning was fo great that he was invited from Athens
to Alexandria by Ptolemy Euergetes, and made by him keeper of the royal
library at that place. It was at his inftigation that the fame Ptolemy ſet
up thoſe armillas or circles of braſs, in the portico at Alexandria, with
which Hipparchus and Ptolemy afterwards fo fuccefs fully obferved the hea-
venly bodies. We are told, by Ptolemy, that he found the diſtance be-
tween the tropics to be eleven fuch parts as the whole meridian contains
eighty-three.
1565 Much about the fame time with Eratofthenes, Berofus, a native of
Chaldea, flouriſhed at Athens. Jofephus, in his anſwer to Apion, tells us
that he was much eſteemed by all lovers of learning for his great know-
ledge in aſtronomy, and the Chaldean philofophy; and that he wrote
many books concerning theſe matters in the Greek tongue, fome of which
are yet extant, wherein he affirms that he had feen at Babylon aſtrono-
mical ephemerides for 480 years infcribed on tyles. It has been fuppofed
that many inventions, now afcribed to the later Greeks, were brought by
this author from Babylon; whilft others again contend that the Greeks
owe little or nothing of their aſtronomical knowledge to the Babylo-
nians.
1566 Archimedes,
CHAP. 7.
679
ASTRONOMY
1566 Archimedes, who, excepting Sir Ifaac Newton, was undoubtedly
the greateſt mathematician, that ever appeared, flouriſhed about 220 years
before the birth of Chrift. The very name of Archimedes conveys to the
mind of a mathematician an idea of the utmoſt extent of human ſubtilty.
He was the firſt who affigned the true area of any curvilinear ſpace what-
foever, which he did by demonftrating, with all the rigour of the ancient
geometry, that the area of every parabola is to that of its infcribed
triangle, as 4 to 3. Nor was his ſkill in aſtronomy, properly fo called,
inferior to what it was in geometry: Macrobius 1. 2. c. 3. fays that he
"determined the diſtance of the moon from the earth, of mercury from
the moon, of venus from mercury, of the fun from venus, of mars from
the fun, of jupiter from mars, and of ſaturn from jupiter; as likewiſe
the diſtance of the fixed ſtars from the orbit of faturn." We learn from
Hipparchus that he made aftronomical obfervations, and in particular
that he obſerved the time of a folftice; and laſtly, it appears from a Latin
epigram of the poet Claudian that he invented a kind of planetarium, or
orrery, to repreſent the phenomena and motions of the planetary ſyſtem.
When Syracuſe was taken by Marcellus in the year before Chrift 211, he
gave particular orders, to all his officers, to treat Archimedes with reſpect
and tenderneſs; but his kind intentions were fruftrated by the brutality
of the foldier, who firſt found him, and flew him, becauſe he was fo in-
tent upon the problem, he was then about, as not to make fuitable an-
ſwers to the queſtions, which he put to him.
1567 Hipparchus, born at Nice in Bithynia, faid, by Ptolemy, to be a
lover of truth and induſtry, ſeems to have been the firſt who applied him-
felf to the cultivation of every part of aftronomy; thoſe aſtronomers who
went before him having confined themſelves chiefly to the motions and
magnitudes of the fun and moon, leaving us very few obfervations of the
planets and fixed ftars. We are told by Ptolemy, 1. 5. that he obſerved
the ſtars at Rhodes, from whence fome have concluded that he was born
there. Others, indeed, have ſuppoſed that there were two aftronomers
of the name of Hipparchus; one a Bithynian, and the other a Rhodian;
but it is no ways improbable that the fame Hipparchus, who was born in
Bithynia, might obferve both at Rhodes and Alexandria; neither is it
unlikely but that, while he was in Bithynia, he might be ignorant of the
motion of the fixed ſtars, and ſo follow Eudoxus in his books on the phe-
nomena of Aratus.
4S
1568 Ptolemy
680
BOOK 5.
ASTRONOMY
1568 Ptolemy farther informs us that Hipparchus had ſuch an accurate
knowledge of the planetary motions as firſt to diſcover that their orbits
were excentric, and that, upon this hypothefis, he wrote a book againſt
Eudoxus and Calippus. He moreover gives us many of his obfervations,
made between the years 160 and 125 before Chrift; and tells us, that by
comparing a fummer folftice, obferved by himſelf, with one obferved by
Ariftarchus, 145 years before, he determined the length of the year with
great exactneſs, and wrote a treatiſe on the fubject. From the fame
fource of information, we learn that it was Hipparchus who firſt found
out the anticipation of the moon's nodes, the excentricity of her orbit,
and that ſhe moved flower in apogee, and faſter in perigee. That he col-
lected fuch ancient eclipfes of the fun and moon, as were obſerved by
the Chaldeans. That he formed hypotheſes, and conſtructed tables of
the motions of the fun and moon; and would have done the ſame for the
other planets, if he could have found ancient obfervations fufficient for
the purpoſe; but not finding fuch, he contented himſelf with collecting
fit obfervations for that purpoſe, and in endeavouring to form theories of
the five planets.
1569 Hipparchus, by comparing his own obfervations of fpica virginis
with thoſe made by Timocharis at Alexandria, 100 years before, firſt of all
found that the fixed ſtars changed their places, and had a flow motion of
their own from weſt to eaſt: he alſo corrected the calippic period, and is
faid to have pointed out fome errors of Eratofthenes in his meaſure of
the earth.
1570 Geometry having by this time been greatly improved and called
in to the aſſiſtance of aſtronomy, Hipparchus was enabled to attempt the
determination of the fun's diſtance from the earth in a more correct man-
ner than had hitherto been done, and a noble attempt it was! But al-
though it diſcovers a vaſt comprehenfion of thought in the contriver, it
is found to be totally uſeleſs, when applied to practice, becauſe it requires
a much greater accuracy in the obfervations than can be attained to. See
Keil's Aftron. p. 258. Ricciol. Almag. nov. 1. 3. c. 7. Ptol. Synt. p. 126.
1571 But the greateſt work of this excellent aftronomer is his cata-
logue of the fixed ſtars, which he was firft induced to begin by the ap-
pearance of a new ſtar. This catalogue, which is happily preferved to
us by Ptolemy, is the oldeſt we have, and contains the longitudes and
latitudes of 1022 ftars, with their apparent magnitudes. Befides the
books abovementioned, he wrote a book concerning the intervals between
eclipfes,
CHAP. 7.
681
ASTRONOMY
eclipſes, both folar and lunar, and is faid to have calculated all that were
to happen for 600 years from his time.
1572 Menelaus was an eminent mathematician and aftronomer, and
made many obſervations of the ſtars and planets, both at Rhodes and
Rome, about the year of Chrift 90. He compoſed three books of ſpherics,
or the geometry neceffary to aftronomy, which fhew great ſkill in the
ſciences, and are very complete. Ptolemy is fuppofed to have taken from
them what he has left on this fubject in the first and fecond books of his
Almageſt. Dr. Halley has given us a fair edition of this work. Menelaus
alfo wrote fix books on chords.
1573 Agrippa, the mathematician, obferved the conjunction of the
moon with the pleiades, November 29th, in the year of Nabonaſſar 840,
or of Chrift 93.
1574 Theon, of Smyrna, fays that the ancients made the moon and
venus to deflect 6 degrees from the zodiac, both ways; but the fun only
one fuch degree as the whole circle contains 360.
1575 It would be very eafy to record the names of a great number of
Greek and other aftronomers, who lived between the times of Hipparchus
and Ptolemy, and chiefly about the beginning of the reign of Antoninus
Pius; but as they made little or no advances in the fcience, I fhall pafs
them by, and come immediately to that prince of aftronomers, Claudius
Ptolemy, of Pelufium; or, as others have it, of Ptolemais in Egypt, and
who is the moſt ancient aftronomer, whofe works have been handed down
It is to his almageft, or the great compofition, that we are in-
debted, not only for his own obfervations, but for almoft all which
remain of Hipparchus, Ariftyllus, Timocharis, and the ancient Babylonians.
to us.
1576 This learned perfon was born in the year of Chriſt 69; and, al-
though the principles upon which his fyftem is founded are erroneous,
yet his work will always be uſeful to aſtronomers on account of the great
number of ancient obfervations which it contains, and will, undoubtedly,
perpetuate his name to the lateft pofterity. It is divided into 13 books:
in the firſt he endeavours to fhew that the earth is at reft in the center
of the univerſe; that it is ſpherical, and but a point in compariſon of
the diſtance of the fixed ftars: he treats of the feveral circles of the earth,
and their poſitions in a right ſphere.
In the ſecond he treats of the habitable parts of the earth, and of the
nature and poſitions of its circles in a right ſphere.
4 S 2
The
682
BOOK 5.
ASTRONOMY
The third book treats of the true length of the year, of the unequal
motion of the fun in the ecliptic, and alfo of the unequal length of days
and nights: it likewife contains tables of the fun's mean motion, and
precepts for ufing them.
In the fourth he treats of the lunar motions; gives tables for comput-
ing them, and exhibits the principles, and obfervations on which they
are founded.
In the fifth he treats of the excentricity of the lunar orbit, and the in-
equalities of the moon's motion: affigns the magnitudes of the fun, moon,'
and earth; and their diſtances from one another.
In the fixth he treats of the conjunctions and oppofitions of the fun
and moon, the limits of folar and lunar eclipſes, and gives tables for
computing the times when they will happen.
In the feventh he treats of the fixed ſtars; deſcribes the various conftel-
lations by means of an artificial ſphere; rectifies their places to his own
time, and fhews how different they then were from what they had been
in the times of Timocharis, Calippus, Hipparchus, and others: and con-
cludes with a catalogue of the ſtars in the northern hemisphere.
The eighth book contains a catalogue of the ſtars in the fouthern he-
miſphere, as alſo a catalogue of the ſtars in the twelve zodiacal conftella-
tions: this catalogue of the ſtars is the oldeſt extant, and therefore con-
ſtitutes a very valuable part of the work. The book concludes with a
diſcourſe on the Galaxy, or milky-way, and an account of the rifing and
fetting of the fun and fixed ſtars.
The ninth book treats of the order of the planets, and of their periodi-
cal revolutions: contains tables of their mean motions; and concludes
with the theory of mercury and accounting for its various phenomena, as
feen from the earth.
Books ten and eleven treat, in like manner, of the various phenomena.
of the planets venus, mars, jupiter, and faturn; and fhews how the tables.
have been corrected from the obſervations of preceding aftronomers.
The twelfth book treats of the ſtationary and retrograde appearances
of the planets; and the thirteenth of their latitudes, the inclination of
their orbits, rifings, fettings, &c.
•
1577 This work was firft tranflated out of Greek into Arabic, about
the year 827, and out of Arabic into Latin, by favour of the emperor
Frederic II. about the year 1230. The Greek text of Ptolemy was not
known in Europe until the beginning of the 15th century, when it was
brought
CHAP. 8.
683
ASTRONOMY
brought from Conftantinople, then taken by the Turks, by George, a
monk of Trapezond, who tranflated it into Latin. This tranſlation was
publiſhed at Venice in 1527, and Bafil in 1541: at the latter place the
Greek text had been printed in 1538, with a commentary by Theon, the
younger, and Pappus, both mathematicians of Alexandria in the fourth
century. In this work Theon fets down an eclipſe of the fun as obſerved
by himſelf, anno Nabon. 1112. After theſe laſt mentioned authors, aftro-
nomy received little or no improvement from the Greeks, if we except
thoſe ſeven books of obſervations, made by Thius about the year 500,
which Bullialdus tells us he found in the library of the king of France.
CHAP. VIII. ASTRONOMY OF THE ARABIANS, PERSIANS AND TARTARS.
1578 From the year 800, almoſt to the beginning of the 14th century,
Europe was plunged in darkneſs, and the moſt profound ignorance; but
during this period ſeveral able men aroſe amongſt the Arabians, and
chiefly at Bagdad, which is very near the ancient Babylon; and fome
uſeful works were performed by them.
1579 In the time of the emperor Heraclius, about A. D. 600, the Arabs,
conquering Syria, Perfia and Egypt, formed an empire which afterwards
extended itſelf into Afia, Africa, and even into Spain. The caliphs of
Babylon were the most powerful princes of Afia, and their dominion
reached to the Indies.
1580 Almanzor, the fecond caliph of the family of Hafchemides, was
ſkilled in many ſciences, and firſt introduced a taſte for ſtudy in his em-
pire. His grandſon Almamon was alſo very fond of the ſciences, and ap-
plied himſelf to the cultivation of them with great affiduity. After he
came to the empire in 814 he ſtill devoted much of his time to the ſciences,
and encouraged them amongſt his fubjects. In a treaty of
In a treaty of peace which
he made with Michael II. emperor of Conftantinople, he ftipulated for
leave to fearch, throughout all Greece, for books of philoſophy, that they
might be tranſlated into Arabic; and in the year 827 he had Ptolemy's
almageſt tranflated. He made many aſtronomical obfervations himſelf,
and determined the obliquity of the ecliptic to be 23° 35. He had alfo
many able men who conſtructed fit inftruments, and uſed them in mak-
ing aſtronomical obfervations: and it was under his. aufpices that a degree
of
น
684
BOOK 5.
ASTRONOMY
*
2
of the earth was meaſured a fecond time, in the plain of Singar, upon
the border of the Red fea, § 465. He died in the year 833.
1581 From this time aſtronomy was ſtudiouſly cultivated by the Arabs;
and Alferganus, who was partly contemporary with the caliph Almamon,
wrote elements of aſtronomy, in 30 chapters; which has been three times,
tranſlated into Latin, and a very curious edit. of it was printed at Amſter-
dam in 1669, with notes by Golius.
1582 But the moſt celebrated of their aftronomers, whofe works have
been handed down to us, was Albategnius, who lived about 880 years after
Chriſt. He is called Muhamed Aractenfis, as being a Syrian of Aracta, or
Racha, in Meſopotamia, though he made fome obfervations at Antioch.
Finding the tables of Ptolemy to want correction, he made new ones,
fitted to the meridian of Aracta, which were long eſteemed by the Ara-
bians. He greatly reformed aftronomy in his book de fcientia ftellarum,
by comparing his own obſervations with thoſe of Ptolemy. Amongst his
diſcoveries, the chief are the motion of the fun's apogee from the time of
Ptolemy to his own: the preceffion of the equinoxes, which he made to
be a degree in about 70 years; for he found it was neceffary to add 11
50' to the places of the fixed ftars, as they ſtand in Ptolemy's Almageſt,
to make them agree with the heavens in his time: that the firſt ſtar in
aries was then diſtant 18° 2' from the equinoctial point: and lastly, that
the fun's greateſt declination was 23° 35'. The original Arabic of his
works was never printed, but lies amongſt the manufcripts in the Vatican
library. It has been tranflated into Latin by Plato Tiburtinus, and printed
at Bononia in 1645, with notes by Regiomontanus.
Q
1583 For fome centuries after the time of Albategnius feveral learned
aſtronomers are found in every part of the Saracen empire; but none of
them have left us any obfervations, of fo much confequence, as three
eclipfes, which were obſerved at Cahir, in Egypt, by Ebn Younis, aſtro-
nomer to the caliph there, A. C. 977 and 978, with ſo much care as to
enable us to determine the quantity of the moon's acceleration fince
that time.
1584 About the year 1260 Naffir-Eddin-Ettufi, a diligent and careful
obſerver flouriſhed at Maraga, a town in Aderbijan. He publiſhed aſtro-
nomical and geographical tables, which he called Tabula Ilchanica, from
a Tartar prince of that name. His table of the latitudes and longitudes
of places was publiſhed by Graves, and may be ſeen amongſt Hudſon's
Geograph. Minor.
1585 Other
CHAP. 8.
685
ASTRONOM Y
1585 Other aſtronomers of note amongſt the Saracens are, Ebenfophi,
author of the Perfian tables: Arzachel, a moor of Spain, who obferved
the obliquity of the ecliptic, § 802; and alfo made tables of fines, or half
chords of double arcs, dividing the diameter into 300 parts: Alhazen, his
contemporary, who wrote upon optics, and in that work firſt fhewed
the importance of the theory of refractions in aftronomy; he alſo wrote
upon the twilight, and the height of the clouds, and explained in a very
ſcientific manner, the phenomenon of the horizontal moon: laftly, Almeon
and Thebet-ben-Chora, exact obfervers of the obliquity of the ecliptic, and
compilers of tables; whom fome authors make contemporary, and others
place in different ages.
1586 Paffing over many others of lefs note, but who, nevertheleſs, all
of them added fomething to what others had done before, we come to
Ulug Beigh, a prince of Tartary, and grandfon to the famous Tamerlane;
who, although he lived fome ages after thoſe laſt mentioned, ſeems to
have had his learning from Perfia. He is faid to have had very large in-
ftruments, and to have determined the celeſtial motions with greater ac-
curacy than
any that went before him: Graves fays, that he had a qua-
drant as high as the roof of the church of St. Sophia at Conftantinople,
which is 180 Roman feet. He compoſed aſtronomical tables, from his
own obſervations, for the meridian of Samarchand, his capital city, fo
exact as to differ very little from thoſe of Tycho Brahe: but his principal
work is his catalogue of the fixed ſtars, made from his own obfervations,
at Samarchand, in the year of the Hegira 841, or of Chriſt 1437. This
catalogue was publiſhed at Oxford in 1665, by Dr. Hyde, with notes.
The accuracy of his obfervations may, in fome meaſure, appear from
hence, that he determined the height of the pole at Samarchand to be
39° 37′ 23″, as we learn from Graves's preface to his tables of the lati-
tudes and longitudes of places, inferted in Hudſ. Geog. Min. v. iii. He
was put to death by his own fon in the 853d year of the Hegira, or the
1449th after J. C. See Pococke's Sup. to Abulfarag. Hift. Dyn. p. 6.
1587 It is, undoubtedly, to the Arabians that we are indebted for the
prefent form of trigonometry; for although Ptolemy rendered the theory
of Menelaus much more fimple, yet he worked by very laborious rules.
Geber, inſtead of the ancient method, propofed three or four theorems,
which are the foundation of the modern trigonometry. The Arabians
alſo made the practice ſtill more fimple by uſing the fines inſtead of chords
of the double arcs, which was one of their firſt inventions; for it is found
in
686
BOOK 5.
ASTRONOMY
in Albategnius; and there is alſo, in the libraries, a treatiſe of Alfraganus
upon the right fines. The Arabians received their ten digits, or nume-
ral figures, from the Indians. Arzakel, author of the Toledo tables, and
one of the firſt, whofe works are come down to us, that uſed thoſe
figures, lived about the year 1080. He was an excellent aſtronomer, for
the times he lived in, and made many improvements in the fcience. He
obferved the obliquity of the ecliptic to be 23° 34′; and has left us a table
of natural fines, in which he divides the diameter into 300 parts, which
Ptolemy divided only into 120.
1588 In the ninth century the Arabians made their way into Spain,
and having intercourſe with all the weſtern parts of Europe, imparted to
them the ſcience of aftronomy, which had for fo many years been totally
loft to that part the world.
CHAP. IX. OF THE RESTORATION OF ASTRONOMY IN EUROPE, AND ITS
PROGRESS FROM 1230 TO 1560.
1589 While the Saracens were thus diftinguiſhing themſelves in the
eaſt by their learning, and labours for the advancement of aftronomy,
there ſcarce appeared one European who deferves to be named in the
hiſtory of that ſcience. But the emperor Frederic II. who reigned about
the year 1230 began to protect and encourage learning. He reſtored the
univerſity of Naples, and founded one at Vienna in 1237; he alſo revived
thoſe of Bologna and Salerno. He caufed many ancient books of phyfic
and philoſophy, particularly the works of Ariftotle, and the almageſt of
Ptolemy, to be tranſlated out of Arabic into Latin. This tranſlation of
the almageſt, made in the year 1230, contributed fo much to the ftudy
and learning of the fidereal ſciences amongſt Europeans, that from thence,
as an epocha, we may date the revival of aſtronomy in Europe.
1590 John de Sacro-bofco (or of Halifax) an Engliſhman, and brought
up at Oxford, is the firft writer who deferves to be taken notice of, after
that time. He flouriſhed about the year 1232, and compiled, out of
Ptolemy, Albategnius, Alferganus, and other Arabians, his four books de
Sphæra; which treat of the ſphere of the world, the celeftial circles, the
proper motions of the ſtars and planets, the rifing and ſetting of the
figns, the diverfity of days, nights and climates, and of the cauſe of
eclipfes. This work was fo celebrated that for 300 years it was preferred
in
CHAP. 9.
687
ASTRONOMY
in the ſchools to any other, and has been thought worthy of ſeveral com-
mentaries, and particularly by Chrift. Clavius, in 1531.
1591 About the year 1240 Alphonfus X. king of Caftile, furnamed the
wife, finding many errors in the tables of Ptolemy, called together many
perfons, learned in aſtronomy, as well Chriſtians, as Jews and Moors,
who met at Toledo, in the lifetime of his father; and, after many con-
ſultations, made new tables, which they called Alphonfine, in honour of
this prince, and publiſhed them in 1252, the firſt year of his reign. They
are faid by fome to have coſt him 40,000, and by others 400,000 ducats.
He died in 1284, aged 81 years. Weid. Hift. Aftron. p. 279.
1592 About the fame time Roger Bacon, a learned Francifcan, at Ox-
ford, wrote many things relative to aſtronomy; particularly of the places
of the fixed ſtars, of the folar rays, and lunar afpects. He wrote alſo a
treatiſe on perſpective, in which he treats largely on the effects of ſpheri-
cal lenfes, both fingle and combined together; although it does not ap-
pear, from his writings, that he had ever thought of fixing them in a
tube, as they are now done in teleſcopes. See Molyneux Opt. p. 256.
Smith's Opt. p. 13. 20. rem.
1593 Soon after this time, namely, about 1270, Vitellio, a Polander,
wrote a treatiſe of optics after the manner of Albazen, fhewing the uſe of
refractions in aſtronomy.
1594 From this time to near the middle of the 15th century, we meet
with few or no improvements in aſtronomy; nor ſcarcely any aſtronomer
worthy of notice, except Profatius, a Jew, who is faid to have obferved
the fun's greateſt declination, and the vernal equinox in 1303. But about
the middle of that century every part of aftronomy was carried on with
fuccefs, and profpered, by the great, the ingenious, and ſtudious George
Purbach, fo named from Puerbach, a town between Auſtria and Bavaria,
where he was born, in 1423. He ſtudied firſt at Vienna, and afterwards
at Rome and Ferrara, where all men were ftruck with his learning, and
clear method of teaching. However, he returned to Vienna, where he
was not only honoured, but had a handſome penſion allowed him by the
emperor. His firſt work was a Latin commentary on Ptolemy's almageſt,
as tranſlated from the Arabic; becauſe he did not underſtand Greek, or
even had a Greek copy of that book. He wrote alſo an introduction to
arithmetic and dialling, with tables for various climates. He alſo made
tables of the proportion of the parallels, at every degree, from the equi-
noctial. He made ſpheres and globes, as well as uſed them; and added
4 T
new
688
BOOK 5.
ASTRONOMY
new tables of the fixed ftars, reduced to the middle of that age. He made
dials and quadrants, and moreover collected many tables of the firſt mo-
tion, to which he added new ones of fines, for every ten minutes (which
Regiomontanus afterwards extended to every minute) making the whole
fine 60, with fix cyphers annexed, after the example of Ptolemy, who
made the greateſt chord, or diameter, 120. He likewife corrected the
tables of the planets, making new equations to them, becauſe the Al-
phonfine tables were very faulty in this refpect. In his folar tables, he
placed the fun's apogee in the beginning of cancer, but retained the obli-
quity of the ecliptic 23° 33', as it had been determined by former aftro-
nomers. He made new tables for computing eclipfes, of which he ob-
ſerved fome, and had juſt publiſhed a new theory of the planets before his
death, which happened in 1461.
1595 John Muller, of Monteregio, (Coningſberg) a town in Franconia,
and thence commonly called Regiomontanus, was a ſcholar of Purbach. In
his youth he learned the doctrine of the ſphere, and was greatly delighted
with aſtronomy; on which account he quickly learned arithmetic and
geometry, and put himſelf under the care of Purbach, then profeſſor at
Vienna; under whom he foon became fo great a proficient in aſtro-
nomy as to fucceed his mafter, who died foon after. He completed the
epitome of Ptolemy's almageft, which Purbach had began; and, in 1461,
on the death of that excellent aftronomer, he went to Rome; where he
made various aftronomical obfervations. He afterwards went to Padua,
and in 1471 retired to Nurimberg, where he was received by Bernard
Walther, a wealthy citizen, and lover of aſtronomy, and who out of re-
gard to that ſcience cauſed ſeveral aſtronomical inſtruments to be made of
brafs, under the direction of Regiomontanus, for obferving the altitude of
the fun and ſtars, and other celeftial phenomena: amongſt theſe was an
armillary aſtrolable, like that which was uſed by Hipparchus and Ptolemy
at Alexandria; and with which Regiomontanus made many obſervations.
He alſo made, ephemerides for 30 years to come, fhewing the lunations,
eclipfes, &c. He wrote of the theory of the planets and comets; and
alſo a treatiſe on triangles, yet in repute for containing divers extraordi-
nary cafes.
cafes. He is likewiſe ſaid to have been the firſt, who introduced the
uſe of tangents into trigonometry, and to have publiſhed, in print, many
of the moſt eminent authors on aftronomy amongst the ancients. To-
wards the latter part of his life he returned to Rome, where he died, at
the age of 40 years, not without fufpicion of being poiſoned by the fons
of
CHAP. 9.
689
ASTRONOMY
of Trapezuntius, the envious oppofers of his merits, and was buried in
the pantheon at Rome.
1596 After the death of Regiomontanus, Bernard Walther, who has been
mentioned above, fought carefully for the inftruments, books and manu-
fcripts which he had left behind him, and which he purchaſed of his
heirs; and continued to obſerve with the armillas and parallactic rulers
until his death, which happened in the year 1504. He was born at Nu-
rimberg in 1430, and though rather the older man, is ufually called the
fcholar of Regiomontanus; for as he began theſe ftudies later in life, it was
later before he became a proficient in them; but being opulent, and wiſh-
ing to retrieve the time that he had loft by every means in his
power, he
put
himſelf under the care and inſtructions of this celebrated aſtronomer,
both in the theory of aftronomy, and the practice of making obfervations.
After the death of Walther, the obfervations which had been made, both
by him and Regiomontanus, were collected, by order of the fenate of Nu-
rimberg, and publiſhed there, by John Schoner, in 1544; again by Snellius
at the end of the obſervations, made by the Landgrave of Heffe, in 1618;
and laſtly, in 1666, with thoſe of Tycho Brahe. We are told by Snellius,
in a note at the end of thoſe obſervations, that Walther complained of his
armilla; and faid that although it was fix feet in diameter, it was not
exact enough to give the obſervations with certainty to less than ten mi-
nutes. Schoner affures us that Walther made uſe of a very good clock,
which would always go well from noon to noon.
1597 In the beginning of the 16th century John Werner flouriſhed at
Nurimberg: he was an excellent aſtronomer, and appears to have been
the greateſt geometer of theſe times. He was born February 14th, 1468;
and from his childhood, as he himſelf tells us, applied himſelf to the
ſtudy of the liberal arts, but particularly to mathematics; being induced
to it by the truth and certainty of that branch of learning. Having been
informed that Regiomontanus made great proficiency in thofe ſciences in
Italy, he went to Rome in 1493, and, while there, was very diligent in
making aftronomical obfervations, and in his application to every
branch
of mathematical learning. On returning to his own country in 1498, he
was admitted into holy orders; and though, by this means, he became
engaged in other duties, he, nevertheleſs, applied himſelf with great
earneſtneſs to the improvement of aftronomy and the mathematics, and
in obſerving and collecting fuch phenomena as feemed to him worthy of
notice. He obſerved the motion of the comet in the month of April
4 T 2
1500,
690
BOOK 5.
ASTRONOMY
1500, and deſcribed it, (See Milichii Comment. in II. Plin. c. xxv. p. 262.)
and publiſhed ſeveral tracts, in which he handled many capital points,
relative to geometry, aftronomy, and geography, in a maſterly manner;
and which met with great applaufe from the learned of thoſe times.
There are yet extant his tranflation, with a commentary annexed, of the
firſt book of Ptolemy's geography, in which he, firſt of any one, propoſed
the method of finding the longitude at fea, by obfervations of the moon's
diſtance from the fixed ſtars, and which is now fo fucceſsfully carried into
practice; a tract concerning four different projections of the fphere in
plano: an explanation of a paffage, in a tract of George Amirufcius, con-
cerning the effentials of geography, from the 7th book of Ptolemy's geo-
graphy, relating to maps: one epiftle of Regiomontanus to Baffario, con-
cerning meteoroſcopes: five books on the conftruction and uſe of me-
teoroſcopes: five books concerning triangles: mifcellaneous problems re-
lating to aftronomy and geography: an analyſis to accompany the book
of Euclid's data: on the doctrine of fhadows: a tract containing twenty-
two propofitions in conics: a commentary, or paraphraſtic diſcourſe,
containing eleven methods of doubling the cube: a commentary on the
problem of Dionyfiodorus relating to the cutting of a ſphere, by a plane,
fo that the two parts may obtain a given ratio: two tracts concerning the
motion of the eighth fphere, or of the fixed ftars: and, laſtly, a ſhort
diſcourſe concerning the theory of the eighth ſphere. The five laſt books
were publiſhed at Nurimberg about the year 1522; but we are here chiefly
concerned about the two laft, in which he has fhewn, by comparing his
own obfervations of the ftars regulus, the virgin's ſpike, and the bright
ftar in the fouthern ſcale of the balance, made in 1514, with the places
of the ſame ſtars as put down by Ptolemy, Alphonfus, and others, that the
motion of the fixed ftars, now called the preceffion of the equinoctial
points, is 1° 10' in one hundred years, and not one degree only, as for-
mer aſtronomers had made it. This tract on the motion of the eighth
ſphere was fo exceeding ſcarce in the time of Tycho Brahe, that he fought
all Germany for it in vain: for this reaſon he wrote to Maginus, requeſt-
ing him to feek for it in Italy, and who having at length found it, ſent
it to him in the year 1591, as Gaffendus teftifies in the life of Tycho, p. 435.
Werner made the fun's greateſt declination 23° 28′, and the diſtance of the
firſt ſtar in aries from the equinoctial point 26 degrees. Moreover, he
collected, and made himſelf a great number of meteorological obferva-
tions, and from thence endeavoured to derive rules which might be uſeful
towards
*
CHAP. 9.
691
ASTRONOMY
towards judging of what weather would happen in future: his general
rules for judging of the changes of the atmoſphere were publiſhed at
Nurimberg in 1546, by John Schoner; and are yet to be met with in fome
libraries. He alſo applied himſelf to mechanics, and with the help of
Andrew Heinlin, an eminent mechanic of thofe days, made a machine
which repreſented the motions of the planets according to the Ptolemaic
hypothefis. Doppelmayer de Mathemat. Nuremb. p. 31. Weidl. hift. Aftron.
P. 334. Aftron. par M. de la Lande edit. 1764, p. 120.
1598 James Faber, born in 1432, wrote a commentary on the ſphere
of John de Sacro-bofco, alſo two books on the theory of the celeftial mo-
tions; in which he explains, compendiouſly, the theory and principal mo-
tions of each planet: it was publiſhed at Paris in 1515, and again at
Cologn in 1516, with an explanation by Christ. Sculpinus, profeſſor of
aftron. at that place. He died in the year 1537, aged 105 years.
1599 Dominic Maria, the friend, and fometime tutor, of the celebrated
Nicholas Copernicus, was born at Ferrara, in the year 1464; and was ma-
thematical profeffor at Bononia from 1484 until his death, which hap-
pened in 1514. He applied himſelf with great affiduity to the making of
celeſtial obſervations; and it was by his example and advice that Coper-
nicus was ſtimulated to a more diligent cultivation of practical aftronomy.
He found the fun's greateſt declination to be 23° 29′; and thought that
the plane of the equator was variable with reſpect to the fituation of
places on the earth, becauſe he found that his obfervations gave the height
of the pole greater by 1° 10′ than had been affigned to it by Ptolemy. See
Snellius, Eratofth. Batavus, b. i. c. 8. who has pointed out his miſtake.
1600 We come next to Nicholas Copernicus, who was born at Thorn,
in Pruffia, January 19th, 1472. This illuftrious aftronomer, after he
had been inftructed at home in Latin and Greek literature, went to Cra-
cow, where he ſtudied philoſophy and phyfic, and obtained a doctor's
degree in that faculty. In the mean time, having from his earlieſt years
been fond of mathematical learning, he attended the public lectures of
Albert Brudzevius, who was then profeffor of mathematics in that univer-
fity, whoſe houſe he used to frequent, and to receive instructions from
him privately in thoſe ſciences. When he had learned the nature and uſe
of the aſtrolabe, and began to have a deeper inſight into aftronomy, and
the hiſtory of thofe illuftrious perfons, who had profeffed it, he was fo
ftruck with the great reputation, which Regiomontanus had acquired there-
by, that he refolved to follow his example; and to that end ftudied it
with
692
BOOK 5.
ASTRONOMY
with unremitting diligence. He likewife applied himself to the ſtudy of
perfpective, and the art of defigning; an accompliſhment which he fore-
faw would be of great ufe to him in his travels, which, about this time,
he began to think of. He went into Italy when he was about 23 years
old, and ſtayed for fome time, firſt at Bologna, on account of the learn-
ing and reputation of Dominicus Maria, a native of Ferrara, and who was
a very eminent profeffor of aftronomy at that time. But Copernicus was
not ſo much the ſcholar of Maria, as an aſſiſtant to him in making his
obfervations; ſo that when he came to Rome his reputation was fcarcely
inferior to that of Regiomontanus; and he was accordingly made profeſſor
of mathematics there, with univerfal applaufe, and made fome obferva-
tions in that city about the year 1500.
1601, Returning, fome years after, into his own country, Lucas Wa-
zelrodius, his uncle by the mother's fide, and at that time biſhop of Warm,
appointed him to be one of the canons of the church of Fruenberg, on
the mouth of the Viſtula, where he applied himſelf with the utmoſt aſſi-
duity to the ſtudy of the heavens, and the motions of the heavenly bodies;
and foon perceived that the hypothefes of the ancient aftronomers, in
which they maintain an uniform motion of the planets round the center
of the equant, was neither conformable to harmony, uniformity, or rea-
fon. This induced him to undertake the labour of reading over the books
of all the ancient philoſophers and aſtronomers that he could procure, in
order to trace out all the fyftems that had been invented, and to obſerve
what probability there was in each: and whether there were any amongſt
them that promiſed more elegance and harmony in the celeftial motions,
and more fymmetry and proportion amongſt the ſeveral parts of the uni-
verſe than that, which without any confideration, had been almoſt uni-
verfally adopted. Two opinions, not very diftant from each other, ſeemed
principally to claim his attention: one was that which is now generally
attributed to Martianus Capella, but by fome to the ancient Egyptians
(§ 1523), in which the fun is placed between the moon and mars, with
mercury and venus revolving round it, as the center of their motions; by
which means their motions were fometimes above, fometimes below the
fun, and fometimes fide-ways; thereby accounting for their ſtationary
appearances, as well as their direct and retrograde motions. The other
was that of Apollonius Pergaus, who placing the fun in the center of his
ſyſtem, made not only mercury and venus, but alſo mars, jupiter and
faturn to perform their periodical revolutions round it; whilft the fun,
and
CHAP. 9.
693
ASTRONOMY
and alſo the moon, revolved round the earth as a center, and which was
alſo the center of the world, as well as that of the fixed ſtars: an hypo-
thefis very nearly the fame with that which Tycho Brahe afterwards em-
braced.
1602 Theſe two hypothefes, as they explained in a very natural man-
ner the direct, retrograde, and ſtationary appearances of venus and mer-
cury, pleaſed him much; and the latter of them was equally fucceſsful
in folving the appearances of the fuperior planets. He felt, however,
fome diffatisfaction, even with the latter of them, becauſe the fun, the
moft glorious body in the mundane fyftem, was not made the center of
the world; and becauſe the earth being in the center, and the fun revolv-
ing round it, not only with an annual, but likewife a diurnal motion,
carried the planets along with it with a motion too rapid to be conceived.
But when he underſtood that the Pythagorean philofophy had removed
the earth from the center, and placed the fun there, as being the moſt
noble and beautiful of the heavenly bodies, and therefore deferving of
the moſt eminent ſtation, he was immediately convinced it produced that
elegance, order and harmony, which he had ſo long been looking for:
ſeeing that the earth, revolving round its own axis in the ſpace of twenty-
four hours, and producing, by this means, the viciffitudes of day and
night, the ſphere of the fixed ftars, and alſo the planetary ſyſtem were
relieved from that rapid motion, which, as he juſtly obſerves, exceeded
all belief. He moreover faw, eſpecially after he had read the works of
that excellent aſtronomer, Philolaus, by fuppofing the earth to have an
annual motion, it followed, that in whatſoever fign of the ecliptic the
earth was moving, the fun would be ſeen in the oppofite one; and thus,
the earth would become a planet, inſtead of the fun; and, as well as mer-
cury, venus, mars, jupiter and faturn, refpect the fun as the center of its
motions. "And I have," fays Copernicus, by frequent and long obfer-
vation, diſcovered that, if the motions of the other planets be compared
with the revolution of the earth, and be eſtimated according to the time,
in which each of theſe bodies perform their revolutions, not only their
feveral appearances will follow from this hypothefis; but it will alſo ſo
connect the order of the planets, their feveral orbits, their magnitudes,
diſtances, and even the apparent motions of the fixed ftars themſelves,
that it will be impoffible to remove any one of thoſe bodies out of the
place, which is affigned to it, without diſordering the reft, and even the
whole univerſe alfo."
<<
1603 Coper-
694
BOOK 5.
ASTRONOMY
1603 Copernicus tells us, that he began to entertain theſe notions, and
to write them down, about the year 1507; but he was not fatisfied with
ſtating only the general nature of his hypothefis, and fhewing that the
appearances in the heavens were, upon the whole, as conformable to it
as to other hypothefes, which had been embraced: he was ambitious to
determine the ſeveral periodical revolutions of the planets in it, and thence
to conſtruct tables of their motions, which might correſpond to their
fituations in the heavens better than thofe of Ptolemy and Alphonfo did.
In order to which, he judged it neceffary to make obfervations, that by
comparing them with the more ancient ones, he might attain to greater
exactneſs; and therefore made himſelf a quadrant, croſs-ſtaffs, like thoſe
of Ptolemy, and alſo an inftrument for obferving parallaxes: this inftru-
ment, he tells us, was in form of an ifofceles right angled triangle, the
two equal fides of which were each four cubits, and its hypothenuſe, or
longer fide was divided into 1414 fuch equal parts as each leg contained
What degree of accuracy theſe inftruments of Copernicus admitted
of may be gathered from what Rheticus fays in the preface to his Ephe-
merides for the year 1551. "If I can be able," fays Copernicus, in a let-
ter to him, "to come within ten fcruples [minutes] of the truth in the
motions of the ftars, I fhall not rejoice lefs, than we are told Pythagoras
did, when he had diſcovered the proportion of the hypothenufe to the two
fides of a right angled triangle." This circumſtance is not unworthy
notice, as it difplays at once the incorrectnefs, with which inftruments
were then made, the rude ſtate of aftronomy, at that time, and the in-
duſtry and improvements of fucceeding artiſts, and aftronomers, who now
eſteem the fraction of a fecond not undeſerving their attention. Depend-
ing, however, on the obſervations, which he was able to make with theſe
instruments, and thofe, which had been made by the ancients, he
completed his work concerning the revolutions of the heavenly bodies,
laying down every thing in a geometrical method, after the manner of
Ptolemy.
1000.
1604 This work, the foundation ſtone, on which ſo glorious a fabric,
as the preſent aftronomy, has been built, is divided into fix books. The
firſt book is divided into two parts: in the former he gives a general idea
of his own hypothefis, and his reaſons for preferring it to any other; and
in the ſecond he handles the doctrine of fines, chords, &c. and delivers
the principles of trigonometry, both plane and ſpherical.
น
In
CHAP. 9.
695
ASTRONOMY
In the fecond book he confiders the doctrine of the fphere; gives a de-
ſcription of the various circles, great and ſmall, which compofe it; their
various interfections, and inclinations one to another, and with regard to
the different inhabitants of the earth. He confiders the right and oblique
aſcenſions of the fun and ſtars, their rifings and ſettings, and the lengths
of days and nights: gives us an account of inftruments for obferving the
places of the ſtars; and a new catalogue of their places, magnitudes, &c.
In the third book he treats of the equinoxes, and folftices, the varia-
tion of the obliquity of the ecliptic, which he fhews to have been conti-
nually varying; ftates the quantity of it at different times; inveſtigates
the length of the folar year; gives us tables of the earth's motion in its
orbit; with a table of the proſthaphærefis, or equation of the center; and
concludes with a diſcourſe on the inequalities of natural days, or the equa-
tion of time, as it is now called.
The fourth book treats of the lunar motions and the various hypo-
thefes, by which the ancients attempted to account for them. He then
proceeds to give a new account of theſe motions, their inequalities and
cauſes; and alſo tables for computing the fame. He next confiders the
latitude of the moon, her horizontal parallax, and the means of diſco-
vering its true quantity; the comparative diſtances of the fun and moon,
and their parallaxes, both in longitude and latitude; and, laſtly, the con-
junctions and oppofitions of the two luminaries, with the doctrine of
eclipfes, their durations, and quantities.
The fifth and fixth books are wholly concerned about the planetary
ſyſtem: he here treats of their number, magnitude, diſtances from the
fun, and the times in which they perform their revolutions. He next
gives an account of their diſtances from the earth, their apfides, the fitu-
ations of their nodes, the excentricities of their feveral orbits, and their
inclinations to the plane of the ecliptic; their mean motions, anomalies,
and the periods from whence they have been deduced: he, moreover, ex-
plains the apparent inequalities of their motions, and accounts for their
direct, ftationary, and retrograde appearances; and he concludes the
whole with tables of the latitude for each planet.
1605 It appears from the life of this illuftrious man, written by Gaf-
fendus, that he had completed this work about the year 1530, and that
what he afterwards did to it was only by way of corrections and amend-
ments of what he had formerly written; but it was with the utmoſt dif-
4 Մ
ficulty,
696
BOOK 5.
ASTRONOMY
ficulty, even in the latter part of his life, that he could be prevailed on
to fuffer it to be publiſhed: not that he envied fociety any benefits which
might be derived from his labours; but, as on the one hand, he was
always very diffident of himſelf; fo, on the other, he forefaw that many
would be offended at the novelty of his doctrines; and, therefore, he
wifhed rather to impart them only to a few felect friends, than, by pub-
liſhing them openly, to raiſe the clamour of the multitude. Overcome,
however, at length by the importunity of his friends, he put the work in
order, addreffing it to the fovereign pontiff, Pope Paul III. in which he
declared the reafons which induced him to comply fo reluctantly with
the advice of his friends; and delivered it into their hands, to publiſh in
whatever manner they thought beft. At the expence of theſe friends it
was printed at Nuremberg, under the inſpection of Schoner and Ofiander,
the latter of whom wrote a preface to the work; in order to palliate, as
much as poffible, fo extraordinary an innovation to the public. In the
mean time its immortal author was attacked by the bloody flux, which
was fucceeded by a palfy in his left fide: he, notwithſtanding, retained
his memory and vigour of mind; and, a few hours before he breathed
his laſt, received a copy of his work, which had been ſent him by Rheti-
cus; but he had then other cares upon his mind, and compoſedly refigned
his foul to God on the 23d of May, 1543; being then in the 71ft year of
his age.
1606 After the death of Copernicus the ſcience of aftronomy received
confiderable improvements from feveral learned men, but particularly
John Schoner, Peter Nunez, or Nonius, Peter Appian, and Gemma Frifius.
Schoner was born at Caroldſtad, in Franconia, January 16th, 1477, and
practifed the mathematics, and eſpecially aftronomy, at Nuremberg;
where, by the advice, and at the recommendation of Melancthon he was
made the firſt profeffor of mathematics in that univerfity. He made many
aftronomical obfervations, two of which being on the planet mercury, in
the year 1504, were of great uſe to Copernicus, in determining the mo-
tion of that planet. See Copernici Revol. Cæleft. 1. v. 30.
He greatly promoted and improved the methods of making aſtrono-
mical obfervations, reformed and explained the calendar, and publiſhed
a treatiſe of cofmography, in which he gave a clear deſcription of the
whole earth, by means of a terreftrial globe. He died at Nuremberg on
the day of his nativity, January 16th, 1547. A complete collection of
his
CHAP. 9.
697
ASTRONOMY
his works was publiſhed at Nuremberg, in 1551, by his fon; and again
at the fame place in 1561. See Doppel-mayer, p. 45. Adami vitæ Philof.
Germ. Weidleri Hift. Aftron. p. 337. De la Lande, tom. i. p. 120.
1607 Peter Nunez, or Nonius, was a native of Alcazar, in Portugal;
and was born in the year 1492. He was royal coſmographer, and pro-
feffor of mathematics in the academy of Coimbra, and tutor to the car-
dinal prince Henry. He applied himſelf very early to the ſtudy of aſtro-
nomy and navigation. But he did not confine himſelf to the theoretical
parts of theſe ſciences alone: he made frequent obfervations of the hea-
venly bodies with ſuch inſtruments as were then in uſe; although he had
but too often cauſe for complaining that they were not ſuch as he could
ufe with confidence. This difagreeable circumſtance put him, no doubt,
on contriving better, and was, probably, the cauſe of his inventing the
aſtronomical quadrant, which is deſcribed in his treatiſe de crepufculis, and
which he contrived to graduate in a new and very ingenious manner, as
follows. He firft defcribed feveral concentric circles on the face of the in-
ftrument, the outermoft of which he divided into 90 equal parts, or de-
grees: the next was divided into 89 equal parts, the next to this into 88,
and ſo on, down to 46. Hence it is eaſy to perceive that the index of
the quadrant muſt reſt, in every obſervation, preciſely upon, or exceed-
ingly near a diviſion, in one or other of the circles; and confequently the
degrees and minutes which are contained in the arch may be known by
computation. His works, publiſhed at Bafil, in 1566, contain (befide
his treatiſe de crepufculis, which was firſt publiſhed, and dedicated to John
III. king of Portugal, in 1542, and a tract, de caufis crepufculorum, which
he tranflated from Gerhard of Cremona's. Greek verfion of Alhazen) two
books on the art of navigation, various aftronomical problems, a treatiſe
on the properties of the rhomb. lines defcribed on a globe, on aſtrono-
mical inſtruments, the deſcription of a nautical plane fphere, the refolu-
tion of a problem of Ariftotle, concerning the motion of a veſſel, driven
by oars, and fome very learned remarks on the theorems of Purbach, in
which he fhews, that Purbach had advanced many things, from others,
which were not true, or but very inaccurately demonftrated. His book
of algebra was printed in the Spaniſh language at Antwerp in 1567-8:
beſide which, he publiſhed alfo de erratis Orontij Finaei, in which he de-
monſtrated geometrically that Orontius was deceived in thinking that he
had fquared the circle, doubled the cube, and performed various other
difficult matters in geometry, when he had found two mean proportionals
4 U 2
between
698
BOOK
ASTRONOMY
5.
BOOK between two given right lines. He died at Coimbra in the year 1577.
See Nichol. Antonij Biblioth. Hifp. tom. iii. p. 476. Weidleri Hift.
Aftron. p. 360. De la Lande, tom. i. p. 143.
1608 Peter Appian was born at Leifnig, in Poland, in the year 1495.
In 1524 he was made profeffor of aftronomy at Ingolftadt, where he
greatly improved that ſcience, and geography, by his obfervations and
writings. His chief work was the Cæfarean aftronomy, which was pub-
liſhed at Ingolstadt in 1540, dedicated to the emperor Charles V. and
Ferdinand, his brother. The fcope of it is to fhew how aftronomical
problems may be reſolved by inſtruments, without either calculations or
tables. He adapts all his examples to the meridian of Ingolftadt, and
puts down the difference of time between that and other places. He,
moreover, fhews how to obferve the places of the ſtars and planets by the
aſtrolabe; how to predict eclipfes, and to deſcribe the figures of them in
plano; illuftrating the whole by proper diagrams. In the fecond part he
deſcribes an aſtronomical quadrant, fhews how to divide it with accuracy,
and alſo the manner of uſing it. The book concludes with the obferva-
tions of five comets. One in the year 1531, from Auguft the 6th to the
23d. The ſecond in 1532, from the 25th of Sept. to Nov. the 20th.
The third in 1533, from the 18th of June to the 23d. The fourth in
1538, from January the 17th to the 21ft, and the fifth in 1539, from
May the 6th to the 17th. In this work he, firſt of any one, remarked
that the tails of comets are always turned from the fun. Befides the
above, he publiſhed a treatiſe on coſmography in 1530, and is faid to
have left Ephemerides from 1534 to 1570 unfiniſhed, and fome other
works concerning arithmetic, algebra and gauging. He died at Ingol
ftadt, on the 21ft of April, 1552. See Albin. Chron. Mifn. p. 350. Adami
vitæ Philof. Germ. p. 141. Weidleri Hift. Aftron. p. 349. and De la Lande's
Aftron. tom. i. p. 142.
1609 George Joachim Rheticus was born in Rhetia on the 15th of Feb-
ruary, 1514. After he had imbibed the firſt elements of the mathematics
at Tigura, he removed to Wittemberg, where he more carefully cultivated
that branch of learning, and became a profeffor in the univerſity at that
place; but in 1539, he gave up his profefforfhip, being induced thereto
by the reputation of Copernicus, and went to attend the aftronomical
lectures and obfervations of that famous man. About this time, in order
that aſtronomical calculations might be made with greater eaſe and accu-
racy, he began to conſtruct his table of fines, tangents and fecants, for
each
CHAP. 9.
699
ASTRONOMY
each minute and ten feconds of the quadrant. In this work he firſt ſhew-
ed the uſe of fecants, or hypothenuſes, in trigonometry; and he greatly
enlarged the uſe of tangents, formerly invented by Regiomontanus: but he
affigned for the radius a much larger number of places, than had been
done before, for the greater exactnefs of calculation. This Herculean
taſk, however, he lived not to finiſh, but it was done by his diſciple Va-
lentine Otho, and publiſhed at Heidleberg in 1594. Rheticus's three books
on triangles were prefixed, and a ſeparate book concerning right angled
ſpherical triangles. The ufe of this work was fo confiderable in aftrono-
mical calculations, that if Rheticus had undertaken no other, his name
ought to have been mentioned with honour in a hiſtory of aſtronomy.
He returned to Wittemberg in 1541, or 1542; and undertook again his
office of mathematical profeſſor in that univerſity, of which he was made
dean. He died at Caffobia, in Hungary, December the 4th, 1576. See
Doppel-Mayer, p. 60. Weidleri Hift. Aftron. p. 360. De la Lande, tom. i.
p. 121.
1610 About the fame time lived Gemma Frifius, an eminent phyfician
and mathematician, at Louvain; and who cultivated aſtronomy with great
affiduity. He wrote a commentary on the coſmography of Appian, which
work was again publiſhed at Antwerp, with many obfervations of eclipfes,
in 1584. He invented and deſcribed an inftrument, which he called an
aſtronomical ring. He publiſhed alſo a tract concerning the conſtruction
and uſe of the terreſtrial and celeftial globes; and began to make the
neceffary aſtronomical obfervations for conftructing new ones, but was
prevented by his fudden death, which happened at Louvain, in 1555.
His fon, Cornelius Gemma, publiſhed an edition of all his works at Ant-
werp, in 1588. He invented and improved feveral other aſtronomical
inftruments, which, though they were not fufficient to make more accu-
rate aftronomical obfervations, were nevertheless applied to very good
purpoſe at fea, and he is remarkable for being the firſt who recommended
a time-keeper for determining the longitude of fhips in long voyages.
CHAP.
700
BOOK 5.
ASTRONOMY
CHAP. X. OF THE IMPROVEMENTS WHICH WERE MADE IN ASTRONOMY
BY THE PRINCE OF HESSE, TYCHO BRAHE, KEPLER AND OTHERS, BE-
FORE THE INVENTION OF TELESCOPES.
1611 About the year 1561, William IV. Landgrave of Heffe, a prince
worthy of immortal praiſe, on account of his knowledge and the en-
couragement which he gave to aftronomy, applied himſelf to this ſcience;
and with the aſſiſtance of Chriſtopher Rothman and Juftus Burgius, the firſt
an aftronomer, and the latter an excellent inftrument-maker, erected an
obfervatory on the top of his palace, at Caffel, and furniſhed it with fuch
inſtruments as were then in uſe: namely, quadrants, fextants, and tor-
quets of braſs, made with the moſt exquifite art. With theſe inftru-
ments he made a great number of careful obſervations, which Hevelius
preferred before thofe of Tycho Brahe; and they were publiſhed by Snellius
in 1618.
From theſe obſervations the prince determined the latitudes and longi-
tudes of 400 ftars, which he inferted in a catalogue, where their places
are rectified to the beginning of the year 1593. Burgius is faid to have
made a globe of filver plates, at the command of the prince, and to have
engraven on it theſe ſtars. Some contend that this prince had logarithms
before Neper thought of them.
1612 Paffing over ſeveral aſtronomers of leſs note, we come next to the
illuſtrious Tycho Brahe, born of noble parents, at Knudſtrop, in Scania, in
the year 1546. His father dying while he was very young, the care of his
education devolved on his mother, who endeavoured to train him up to
knowledge and virtue; and his filial obedience and remarkable improve-
ment, in his younger years, ſo far recommended him to his uncle, George
Brahe, who had no children of his own, that he adopted him for his fon,
and placed him under the care of ſkilful tutors, until he was 16 years of
age; and then fent him to Leipfic. During the three years which he re-
fided at this place, he applied himſelf, contrary to the intentions of his
friends, to the ſtudy of the heavens with great affiduity; and foon found
that both the Alphonfine and Prutenic tables differed greatly from the hea-
vens, and eſpecially in mars. He obferved the great conjunction of ſa-
turn and jupiter in the year 1563; and although his inftruments were by
no means fuch as gave him fatisfaction, they were fufficient to convince
him, that the time of this phenomenon, computed from the tables, dif-
fered
CHAP. IO.
701
ASTRONOMY
}
t
fered widely from the truth. About this time he procured a croſs-ſtaff of
wood, made in the manner that had been deſcribed by Gemma Frifius, with
which he obferved the ſtars, frequently for whole nights together, enter-
ing the obfervations with great care and exactnefs in a book, which he kept
for the purpofe.
C
1613 He was called away from Leipfic in May 1565, by the death of
his undle, but remained no longer with his relations and friends than was
neceffary to fettle his affairs, finding them much diffatisfied with him on
account of his applying fo much of his time to the ftudy of aftronomy.
He therefore left them, and went to Wittemberg; and foon after to
Roftock; where, in April 1567, he obferved the folar eclipfe, which is firft
mentioned in his progymnafmata. He went from this place to Augſburg
in 1569, where he made a quadrant which was capable of fhewing angles
to fingle minutes. He also made a fextant of wood which was four
cubits radius.
very
1614 He returned from this pilgrimage in 1571 to his native country,
where he found a patron and an encourager of his ftudies in his mother's
brother; who gave him an habitation at Herritz-wadt, near Knudſtrop,
convenient for the purpoſe of making aſtronomical obfervations. It
was here that he diſcovered and obferved the new ftar, which then ap-
peared in Caffiopea's chair: this ftar fhone for fome months with fuch
brightneſs, as to be ſeen in the daytime; but it died away gradually, and
became extinct in 1574. It was obſerved by the aſtronomers of that day
in almoſt every part of Europe, and in particular by Tycho, who affures
us he loft no opportunity of meaſuring its diftance from other ftars in
that part of the heavens, and has given us a very particular account of
his obfervations in the first book of his progymnaſmata.
1615 From this ſtar Tycho, like another Hipparchus, took occafion to
make a new catalogue, which contained the places of 777 fixed ſtars,
rectified to the beginning of the year 1600. But instead of the moon,
which was uſed by the ancients to connect the places of the fun and ſtars,
Tycho ſubſtituted venus, as having little or no parallax, and yet being,
like it, vifible both in the day and night: the manner in which he con-
ducted his obſervations, as well as the process by which he deduced the
places of the ſtars from them, is fhewn in his progymnaſmata.
1616 While thefe things were in hand, Frederic II. king of Denmark,
to whom the Landgrave of Heffe had recommended Tycho, as a young
nobleman of great merit, gave him the iſland of Huenna, which lies op-
11
pofite
:
702
BOOK 5.
ASTRONOMY
pofite to Copenhagen, for an aftronomical retreat; and furniſhed him
with money for building an obfervatory, for inſtruments, and for the
ſupport of himſelf and family. In confequence of this munificence, the
firſt ſtone of the obfervatory, afterwards called Uraniburg, was laid Aug.
the 8th, 1576, and finiſhed with great expedition. The building was
ſquare, one fide of it being about 60 feet in length, and on the eaſt and
weſt fides there were two round towers, each 32 feet in diameter. No
expence was fpared in the conftruction of the inftruments, which were
fo large and folid, and of fuch exquifite workmanſhip as no aſtronomer
had ever ſeen before. They confifted of quadrants, fextants, circles, femi-
circles, armillæ, both equatorial and zodiacal, parallactic rulers, rings,
aſtrolabes, globes, clocks and fun-dials. Thefe inftruments were fo di-
vided as to fhew fingle minutes; and in fome, the arch might be read off
to ten feconds. Moſt of the divifions were diagonal, but he had one
quadrant divided according to the method of Peter Nonius; that is, by
means of 47 concentric circles. The whole expence is faid to have
amounted to 200,000 crowns.
It may not be amifs to obſerve here that the method of dividing by
diagonals, which Tycho fo much and ſo juſtly admired, was the invention
of Mr. Richard Chanceler, an Engliſhman; as appears from an ingenious
little tract, publiſhed by Thomas Digges, Efq; at London, in 1573, in-
titled Ala feu fcale mathematica. Tycho, however, takes notice that this
method of dividing is not accurately true, when the circles are at equal
diſtances from one another, and gives a method of correcting the error,
from Joannes Ferrerius, by means of circular diagonals, which, if conti-
nued, would all paſs through the center of the inſtrument.
1617 Tycho obſerved at Uraniburg from 1576 to 1597, but he did not
begin to obferve with the new inftruments before the year 1582. In this
retirement he was vifited by foreigners of the higheſt rank and diſtinction,
who honoured him with the moft flattering marks of their approbation
and regard: particularly by James VI. king of Scotland, and afterwards
of England, who made him feveral noble prefents, and wrote a copy of
Latin verſes, in honour of him, which are ſtill extant. But theſe marks
of diſtinction did but ferve to haften his misfortunes; for on the death of
his illuſtrious patron Frederic II. this excellent philofopher began to feel,
very feverely, the effects of jealoufy, which fome perfons had conceived
againſt him; who could not bear to fee fo many favours conferred upon
him, and that foreigners, of fuch high rank and diftinction, ſhould ſo
frequently
CHAP. IÓ.
703
ASTRONOMY
vifit him. They therefore repreſented to the young king that the treaſury
was exhauſted, and, confequently, that it was neceffary to retrench a
great number of penfions, which had been granted for uſeleſs purpoſes;
and in particular that of Tycho Brahe, who had enjoyed it a long time,
and therefore it was high time it was refumed, and given to fome other
perfon, capable of doing more important fervices to the ſtate. In confe-
quence of theſe repreſentations he was difpoffeffed of the fiefs of Norway,
and the prebend of Rotfchildren; which had been granted him for the
ſupport of himſelf, and to defray the expence of his experiments and ob-
ſervations; and as his own eſtate was not fufficient for theſe purpoſes, he
reſolved to look out for fome proper retreat, and in the mean time re-
moved to Copenhagen, with fuch of his inftruments as were moſt port-
able, and continued his obſervations there until Chriftopher Valkendorf, the
chamberlain of the king's houfhold, procured an order for him to diſcon-
tinue them. Upon this he removed to Roſtock, and from thence to his
friend Henry Ranzou, in Holſtein, through whofe intereft with the elector
of Cologne, he was introduced to the emperor Rodolphus. It was to faci-
litate this introduction, and while he fojourned with his friend Ranzou,
that he publiſhed his Aftronomia inftaurata Mechanica, which is dedicated
to his imperial majefty, knowing that he was fond of mechanics, and
other matters of that kind. By theſe means he obtained orders to attend
the emperor, who was then in Bohemia, and from whom he met with a
moſt friendly reception. He had a magnificent houſe affigned him,
together with a penfion of 3000 crowns. Here he renewed his aftrono-
mical obſervations; and the famous John Kepler became his fcholar and
affiſtant. But fuch is the inftability of all human affairs, he did not en-
joy this happy fituation quite three years, before he died of a retention
of urine; being carried off on the 24th of October, 1601, in the 55th
year of his age.
1618 It is well known that Tycho was the inventor of a new ſyſtem of
the world, which he vainly endeavoured to eſtabliſh on the ruins of the
Copernican ſyſtem. He is alfo faid to have been given greatly to the ob-
ſervation of omens, and to be tinctured with a belief in judicial aſtrology.
But theſe points only add to the many proofs, which we already have,
that the greateſt of mankind have their weakneffes; and that human na-
ture is ever fubject to error. His works, which are numerous, will ever
be a lafting proof of his vaſt abilities. They were collected, and printed
at Francfort, in 1648, in 4to.
4 X
After
704
BOOK 5.
ASTRONOMY
After the death of Tycho, the caſtle of Uraniburg did not long remain
entire: for in 1652, when M. Huet went that way to Sweden, it was
almoſt level with the ground; and but few traces of the walls could be
diſcovered. The inhabitants, even the paftor of the church, had never
heard of the name of Tycho or Uraniburg. One old man only, who had
been a fervant in his family, and had wrought at the building, recollected
theſe names!
1619 Of all the pupils and affiſtants of Tycho, while he refided at Ura-
niburg, Longomontanus ſeems to have been his favourite, and to have pro-
fited moft by his inftructions. He affifted him greatly in reforming the
catalogue of the fixed ſtars, and in his theory of the moon: and after his
departure from Denmark, he joined him again in Germany, and affifted
in finiſhing the latter of theſe works. He afterwards returned to his na-
tive country, and was made mathematical profeffor at Copenhagen; where
he acquired great reputation by his aftronomical labours and writings,
The principal of his works, which have come down to us, is his Daniſh
aſtronomy; which contains all the diſcoveries that had been made by
Purbach, Regiomontanus, and Tycho Brahe, together with fome improve-
ments of his own. This work was printed in 1621. Some have afferted
that he was acquainted with the nature of logarithms before they were
thought of by Neper; and even that Neper had fome hints concerning
them from Longomontanus, by means of Dr. Craig, a Scotchman, to whom
Longomontanus had communicated them. This, however, is not probable,
as Longomontanus lived many years after the diſcovery of logarithms, by
Neper, was publicly known, and yet never made any claim to the inven-
tion. He died in 1647, in the 85th year of his age.
1620 John Kepler, who will always be remembered by aſtronomers, on
account of the important diſcoveries, which he made in the ſcience, was
born at Wirtemberg, in or about the year 1530. He began to ſtudy
aſtronomy very early, and had a particular turn for feeking analogies and
harmonies in nature, after the manner of the ancient Pythagoreans; and
having, as he thought, diſcovered a very curious one, he publiſhed an
account of it in 1596, and ſent one of his books to Tycho Brahe. But
although Tycho diſapproved of the ſubject, he ſaw ſo much ingenuity in
the book, that he invited him to refide with him at Prague, after he had
put himſelf under the patronage of the emperor. Here he had before him
all the obſervations of that great man, which contained an ample field for
him
CHAP. 10.
705
ASTRONOMY
him to employ his genius upon for the diſcovery of analogies; and with
more probability of fuccefs than he had done before.
1621 He foon found that aſtronomers had all erred in fuppofing that
the orbits of the planets were circular, and their motions uniform; on the
contrary he ſaw, from the obſervations, that they all move in ellipfes,
which have one of their foci in the center of the fun; and that their mo-
tions are all unequal, varying fo, that a ray, ſuppoſed to be always drawn
from the planet to the fun, deſcribes equal areas in equal times. But it
was not till feveral years afterwards that he made his notable difcovery, of
the analogy, which fubfifts between the diſtances of the feveral planets,
from the ſun, and the periods, in which they perform their revolutions
round it. He tells us that he formed in his mind a multitude of different
proportions between theſe two things, all which he found to be impoffible
in nature, when he came to apply them to the obſervations of Tycho; and
that it was not until the 15th of May, 1618, he difcovered that "The
fquares of the periodic times were as the cubes of their mean diſtances
from the fun."
1622 The fagacity of Kepler, joined to his continual meditations on the
planetary motions, certainly fuggefted to him fome hints of the true prin-
ciple, from which theſe motions flow. For, in the preface to his Com-
mentaries concerning the planet mars, we find him ſpeaking of gravity as
of a power that is mutual between bodies: and he tells us, that the moon
and earth tend towards each other, and that they would meet in a point,
which is fo many times nearer to the earth than it is to the moon, as the
earth is greater than the moon, if their projectile motions did not prevent
it. He adds, that the tides arife from the gravity of the waters towards
the moon. It does not appear, however, that he adhered ſteadily to theſe
notions, but adopted others afterwards; for in his epitome of aftronomy,
publiſhed many years afterwards, he gives us a phyfical account of the
planetary motions derived from other principles.
1623 The writings of this excellent aftronomer are, The Cofmogra-
phical Myſtery, publifhed in 1596. Optical Aftronomy, 1604. Account
of a new ſtar in Sagittarius, 1605. Commentaries concerning the planet
Mars. Nuncius Sidereus, of Galileo, 1610. Ephemerides from 1617 to
1620. Copernican Aftronomy in 1618 and 1622. The Harmony of
the World, and three books on Comets, 1619. The Rodolphine Tables,
1627. But befide thefe he wrote feveral ſmall tracts on the fubjects of
4 X 2
geometry,
706
BOOK 5.
ASTRONOMY
geometry, trigonometry, and logarithms; alfo a Treatife on Dioptrics,
which was, very defervedly, efteemed at that time. The time of his
death is not known with certainty. See Weidl. p. 413.
1624 Contemporary with Tycho and Kepler, lived Mr. Edward Wright,
and John Neper, baron of Merchiſton. To the firſt of theſe we owe ſeve-
ral very good meridional obſervations of the fun's altitudes, made with a
quadrant of 6 feet radius, in the years 1594, 1595, and 1596; from
which he greatly improved the theory of the fun's motion, and computed
more exact tables of his declination than any perfon had done before.
But this ingenious man is better known to the world for his excellent
improvements in navigation, which he publiſhed in 1599, under the title
of <<
Certain Errors in Navigation detected and corrected." To the lat-
ter we are obliged for the invention of logarithms. A diſcovery which,
as the late Dr. Halley juſtly obſerves, was one of the moſt uſeful, that has
ever been made in the art of numbering! Accordingly, we find that the
inſtant it was made public, it met with an univerfal reception, and ap-
plauſe, from the learned of every nation in Europe. At home, the ſub-
ject was purſued with the moſt unremitting diligence by its illuftrious
author, Mr. Briggs, Mr. Gellebrand, Mr. Gunter, and many others; and
abroad, it was taken up by Benjamin Urfinus, Kepler, Adrian Vlacq, and
Peter Cruger; ſo that in a few years after the diſcovery, tables of loga-
rithms were printed more extenfive, than the preſent highly improved ſtate
of aftronomy requires.
1625 About the fame time alfo lived John Bayer, by birth a German;
but hiſtory affords us nothing farther concerning him. His name will,
nevertheleſs, be for ever memorable in the annals of aſtronomy, on ac-
count of his work entitled Uranometria; which is a very complete celeſtial
atlas, or a collection of charts of all the conſtellations, which are viſible
in Europe. To this he added a nomenclature, in which the ſtars in each
conſtellation are marked with the letters of the Greek alphabet; and by
this means every ftar in the heavens may be referred to with the utmoſt
preciſion and readineſs. See Weidleri Hift. Aftron. p. 428. and De la
Lande's Aftron. vol. i. p. 143.
1626 About this time aftronomy was cultivated by many other perfons,
beſide thoſe mentioned above, particularly John Anthony Maginus, Gerard
Mercator, Chriftopher Clavius, Francis Maurolycus, Joannes Homelius, Bar-
tholomew Schultet, and Simon Stevin, abroad; and by Thomas and Leonard
Digges,
CHAP. 11.
707
ASTRONOMY
Digges, John Dee, and Robert Flood at home; but as none of them made
any confiderable improvements in the ſcience, it may be fufficient to have
mentioned their names..
CHAP. XI. THE HISTORY OF ASTRONOMY FROM THE INVENTION OF TE-
LESCOPES TO THE END OF THE SEVENTEENTH CENTURY.
1627 Befide the invention of logarithms, which has been mentioned in
the foregoing chapter as contributing in ſo eminent a degree to the ad-
vancement of aſtronomy, the beginning of this century was remarkable
for another diſcovery of no leſs importance to it—the invention of tele-
fcopes. It does not, at prefent, appear with certainty when, or by whom,,
this noble inſtrument was first thought of: it is nevertheleſs certain that
the invention is modern; for we no where find that optic glaffes, of any
kind whatever, were known to the ancients. Some contend that Alex- ·
ander de Spina, a native of Piſa, firſt made the uſe of glaffes, fo combined,
known to the world: but it feems highly probable that our countryman
Roger Bacon, who died at leaſt twenty years before him, was acquainted
with theſe things firft. For it appears very plainly from Bacon's writings,
that he was well acquainted with the properties both of convex and con-
cave lenſes, not only when confidered ſeparately, but alſo when combined
together in fome fuch manner, as they are now done in teleſcopes. He
no where, however, gives directions for placing thoſe glaffes, either in a
tube or otherwiſe; and it is pretty evident, from the manner in which he
expreffes himſelf, that he had never done it, but wrote only from theory,
The firſt teleſcope, that was actually made, is ſuppoſed to have been the
production of Zachary Johannides, a native of Middleburg, in Zealand;
and that it was made towards the latter end of the fixteenth, or the be-
ginning of the feventeenth century. This is, nevertheless, controverted,
and the diſcovery claimed by John Lipperhoy, another mechanic of the
fame place. But, let theſe conteſted claims ftand how they will, it is
very
certain that Galileo, who was born at Florence in the year 1564, and
who, on account of the many eminent diſcoveries and improvements
which he made, deferves to be efteemed the morning ftar of this century,
which afterwards produced fo many bright luminaries in every branch of
ſcience, reinvented it, without any other affiftance, than that of hearing
fuch
708
BOOK 5.
ASTRONOMY
fuch an inſtrument had been made. For being at Venice in the year
1609, a vague report was ſpread, that a very curious perſpective glaſs had
been fhewn in Holland, by the help of which, vifible objects, though at
an exceeding great diſtance, would appear as if they were very near. The
furpriſing effects of this inftrument, though believed by fome, were diſ-
credited by moft; but the report was fufficient to fet the inquifitive mind
of Galileo at work to find out, how fuch a thing might be effected, and an
inftrument made, fimilar to that which report faid had been ſhewn in
Holland. By confidering the properties of refracted rays, he ſaw that if
he took two optic glaffes, both of them plane on one fide, but on the
other fide, one of them a ſpherical convex, and the other a ſpherical con-
cave, and placed them at a proper diſtance from each other; by applying
his eye to the concave glafs, objects would be feen three times nearer,
and nine times greater, than when feen naturally. But by altering the
focal lengths of the two glaffes, he foon made a teleſcope which magnified
60 times; and, as he ſpared neither labour nor expence, it was not long
before he produced one, which magnified near 1000 times, and made ob-
jects appear more than thirty times nearer.
1628 This account is given by the great inventor himſelf, in which he
neither attempts to arrogate to himſelf more, than was juſtly his due,
nor to detract from the merits of thofe, who had made inftruments of
this kind before him. He adds, that he firſt amuſed himſelf by looking
at terreſtrial objects; but he foon left earthly things, and carried his
views to the heavens: first to the moon, as being neareſt to us, and after-
wards to both fixed ſtars and planets, which he often contemplated with
delight.
He readily perceived ſpots in the face of the moon, from which he con-
cluded it was not ſmooth, equal, and ſpherical, but unequal and rough;
having hills and valleys like our earth. He alſo diſcovered that venus put
on the fame phaſes with the moon; being ſometimes round, fometimes
horned, and at others gibbous. That jupiter had four ſmall ſtars con-
ftantly attending on him, to which he gave the name of Medicean ſtars,
in honour of the duke de Medicis, his patron, and who was, at that time,
the Mæcenas of every learned man (fee § 1098). He alfo difcovered (as
he imagined) that faturn was either compofed of three bodies, or, as he
expreſſed it, was in the ſhape of an olive; for it did not occur to him that
the two extreme parts, which he faw, were the anfe of a ring (§ 1126).
From
CHAP. II.
709
ASTRONOMY
From the ſpots in the fun, firſt ſeen by him, he demonſtrated that that
immenſe body revolved about an axis; and he diſcovered, alfo, that the
via lactea and nebuloſe ſtars were only congeries of numberleſs ſmall ſtars.
1629 It was not until a confiderable time after the fatellits of jupiter
had been diſcovered, that Galileo, and others after him, thought of ap-
plying them to the purpoſe of determining the difference of longitude be-
tween diſtant places. Before this diſcovery, the longitudes of places on
the earth were put down, in maps, from the uncertain eſtimate of travel-
lers, formed from the time, which was ſpent in going from one to ano-
ther. The profpect of being able to determine this important point in
geography by aftronomical obſervations, joined to the hopes, which were
entertained of rendering their frequent immerfions and emerfions uſeful
for the fame purpoſe at fea, was a fufficient inducement to aftronomers
to uſe all that diligence, with which they have endeavoured to complete
the theory of their motions.
1630 M. de Peirefc, upon hearing of the diſcovery of theſe fatellits,.
began to form hypotheſes, and attempted to make tables of their mo-
tions; in which buſineſs he employed many learned men, and amongſt
others M. Morin, who afterwards wrote feveral treatifes on the ſubject of
finding the longitude by other methods. This laft mentioned Gentle-
man having invented a mechanical method of diſcovering the places of
the fatellits, made fome trials of it himſelf, but not finding them an-
fwer, his method was never made public. He was firmly of opinion, that
if the times of the configurations of theſe fatellits were obferved at dif-
ferent places, the difference of longitude between thofe places would be
afcertained by it; but after a multitude of fruitlefs trials to effect this,
he entirely abandoned the undertaking, in hopes that Galileo and Kepler,
both of whom he heard were intent upon the ſubject, might have better
fuccefs. Galileo was himſelf fo confident of fucceeding in the reſolution
of this arduous problem, by means of theſe obſervations, that he actually
began a treaty with the Dutch for doing it; that ftate having then been
long intent on diſcovering the longitude at fea; but he did not live to
make any confiderable advances in this buſineſs.
1631 Reineri, who fucceeded Galileo in this work, under the protection
of the grand duke of Tuſcany, continued his obfervations on the fatellits
of jupiter for many years; and intended, no doubt, to have made tables
of their motions, as he promiſed them to the public, when he publiſhed
his firſt edition of the Medicean tables, in the year 1639. But in a ſecond
edition
710
BOOK 5.
ASTRONOMY
edition of thoſe tables, which he publiſhed nine years afterwards, with
many additions and corrections, he fays not a word of his tables of the
fatellits; which makes it probable he found the conftruction of them at-
tended with greater difficulty than he at firft imagined; and it is not
known what was the refult of all the pains which he had taken for ſo long
a time concerning the fatellits, as all that he had written on this fubject
was loft at his death, notwithſtanding the care which the grand duke took
to have his papers fought after.
1632 The tables, which were made, fometime after the death of
Reineri, by Hodierna, were built on the obſervations of ſo ſmall a num-
ber of years, that they were, in a little time, totally incapable of giving
the configurations of the fatellits near the truth; and Marius was in fo
much hafte to publiſh his tables before Galileo publiſhed any, that he fuc-
ceeded yet worſe.
1633 It was not till after many obfervations had been made on the
fatellits, firſt by different obfervers in the fame place, and afterwards in
places which were remote from each other, that Caffini was able to pro-
nounce, with any degree of certainty, what appearances of the fatellits
were moft proper for determining the longitudes of places; but by many
trials it was found that the entrance of the fatellits into the fhadow of
jupiter, and their exit out of it, are by far the beſt for that purpoſe. And
particularly that the firſt ſatellit furniſhes the moſt exact obſervations, as
being the quickeſt in its motions, and paffing the most directly into and
out of the ſhadow of the planet: that, next to theſe eclipfes, the con-
junctions of the fatellits with jupiter, or with one another, may be made
ufe of; eſpecially when any two of them, moving in contrary directions,
meet each other. And, laftly, that obfervations of the ſhadows of the
fatellits, which may be ſeen to paſs over the diſk of jupiter, are uſeful;
as are alſo the ſpots, which appear on his face, and are carried along it
with greater velocity, than has hitherto been difcovered in any other of
the heavenly bodies.
1634 But while aftronomers were intent on fettling the theory of the
motions of this newly diſcovered fyftem of bodies, mathematicians were
not leſs earneſtly employed in promoting the knowledge, and extending
the uſe of the other diſcovery, which had graced the beginning of this
century. Benjamin Urfinus, an excellent mathematician of Brandenburg,
calculated much larger tables of logarithms, than had been done by their
noble inventor, and publiſhed them in 1625. But Henry Briggs, Savil-
lian
CHAP. II.
711
ASTRONOMY
lian profeffor of geometry at Oxford, after confulting with Neper, calcu-
lated them on a different plan, much more convenient for uſe than that,
which had firſt been thought of by the inventor; making unity the loga-
rithm of ten. Briggs publiſhed this work at Oxford in 1624, under the
title of Arithmetica Logarithmica. It contained the logarithms of numbers
from 1 to 20,000, and from 90,000 to 100,000, to fourteen places of
figures, beſide the index. The fame work was again publiſhed at Goude,
in 1628, by Adrian Vlacq, with the addition of thoſe chiliads, which had
been omitted by Briggs: but in this publication the logarithms were put
down to no more than ten places below the integer. To theſe were fub-
joined the logarithmic fines, tangents and fecants, for degrees and mi-
nutes, to the fame number of places.
1635 Briggs proceeded to calculate a logarithmetical trigonometrical
canon, fuited to that, which he had before publiſhed for abſolute num-
bers, and to the fame number of places. This table was calculated for
degrees and centeſms of degrees; and contained only the fines and tan-
gents, as he thought the fecants might well be fpared. He intended to
have added a treatiſe on the properties and uſe of theſe numbers, but dying
before this was finifhed, or the other publiſhed, Mr. Henry Gellibrand
ſupplied what was wanting, and publiſhed the whole in 1633, under the
title of Trigonometria Britannica. In the fame year another canon of loga-
rithmic fines and tangents was publiſhed by Adrian Vlacq, at Goude, for
degrees, minutes, and ten feconds; extending, like his former, to ten
places of figures befide the index. This work is now become extremely
ſcarce; but we have the logarithms of Briggs and Vlacq publiſhed in one
volume in 4to, at London, in 1742, by William Gardiner, though only to
ſeven places of decimals, which is in many hands: this, however, begins
to be ſcarce, and rarely to be met with.
1636 About the year 1633, Jeremiah Horrox, a young man of very ex-
traordinary talents, turned his mind to the ſtudy of aftronomy, and by
correcting the errors in the tables of Landberg and Kepler from his own
obfervations*, he diſcovered that the planet venus would pafs over the
diſk of the fun, on the 24th of November, 1639, O. S. Of this fingular
phenomenon, he advertiſed his friend Mr. Crabtree, who lived at fome
diftance from him in a letter dated October the 26th, 1739; defiring, at
the fame time, that he would prepare for obferving it with all poffible
attention. Accordingly theſe two were the firft fince the creation of the
* Horrox's Pofthumous Works, publiſhed by Dr. Wallis.
4 Y
world,
712
ASTRONOMY
BOOK 5.
world, who had the fatisfaction of feeing this extraordinary phenomenon.
A very particular account of this obfervation, and the method in which
it was made, was written by Mr. Horrox, and publiſhed, after his death,
by Dr. Wallis: it was again publiſhed by Hevelius, together with a tract
of his own, entitled Mercurius in fole vifus. Beſide this obſervation of the
tranfit of venus, from which Horrox greatly improved the theory of the
motions of that planet, he made many other aſtronomical obſervations,
and alſo formed a new theory of the moon, fo ingenious in itſelf, as to
attract the notice and praiſe of Sir Ifaac Newton. This excellent
man died the 3d of January, 1640, in the 23d year of his age.
young
1637 About the year 1638 many learned men began to affemble them-
felves together and hold conferences on different ſcientific fubjects at Paris.
This practice was firſt ſet on foot by Merfennus. And foon after, Mr.
Oldenburg coming over to England, introduced the fame cuftom here.
This laid the foundation for the Royal Society, which was incorporated
by king Charles II. in 1660; and in 1666 the king of France formed the.
Royal Academy of Sciences into a regular fociety.
1638 About this time, too, flouriſhed that great man John Hevelius,
conful of Dantzic, whoſe name is enobled by his many curious and
learned works. In 1641 he built an obfervatory in his own houſe, at
Dantzic, and furniſhed it with excellent inftruments of his own conſtruc-
tion; particularly octants and fextants of brafs, of 3 and 4 feet radius,
as well as teleſcopes, with which he conſtantly obferved the ſpots and
phaſes of the moon, and from which obfervations he afterwards compiled
his excellent and beautiful work entitled Selenographia. This noble build-
ing, together with all the inftruments and books which it contained, was
deſtroyed by fire on the 26th of September, 1679; but the memory, as
well as the form and conftruction of the inftruments, is preferved in a
curious work of the ingenious inventor, entitled Machina Cæleftis, although
almoſt the whole impreffion of this work was involved in the fame fate
with the inftruments, which it was intended to have eternized. The
damage which Hevelius fuftained by this dreadful accident was eſtimated
at 30,000 crowns.
1639 Upon a diſpute which arofe between Hevelius and that celebrated:
Engliſh mechanic Dr. Hooke, concerning the advantages of teleſcopic
fights, which Hevelius did not uſe, Dr. Halley, who was juſt then returned
from St. Helena, where he had been to obferve and form a catalogue of
the ſtars in the fouthern hemifphere, at the inftance of the Royal So-
ciety,
CHAP. II.
713
ASTRONOMY
t
ciety, vifited Hevelius; and May 16th, 1679, found only a few ſeconds
difference in meaſuring the diſtance of the fixed ſtars, ſpica virginis and
regulus three feveral times. June the 5th, in the morning, Halley ob-
ferved an occultation of jupiter by the moon with Hevelius; and they de-
termined the moon's diameter to be 30′ 53″. Halley owns that feveral re-
peated obſervations, made with Hevelius's inftruments, differed but a very
trifling part of a minute from each other. At this time, when the fupe-
riority of teleſcopic fights is ſo far eſtabliſhed by experience, that no other
have for many years been uſed, the names of theſe two great men may be
fcarcely fufficient to procure credit to this degree of accuracy in their ob-
fervations, with thoſe who are not acquainted with the manner, in which
the fights of Hevelius's inftruments were conftructed: I fhall therefore give
the following fhort account of them.
In the inftruments, which Hevelius ufed, the fight next the eye was a
plane, furniſhed with two flits, exactly parallel to each other, and per-
pendicular to the plane of the inftrument; both of which was made ufe
of in each obſervation. The fight moſt remote from the eye was a cy-
linder, the diameter of which was exactly equal to the distance between
the two flits in the fight next to the eye. Now it is evident, that a little
before the ſtar came exactly into the direction of the fights, it would be
ſeen through one of the flits, but would be hid 'from the eye, when ap-
plied to the other, by the cylinder, which formed the remoter fight.
When the ſtar had paffed the direction of the fights it would be hidden
from the flit, which it was viſible through before, and would then be ſeen
through the other: but in the intermediate fituation between theſe two;
that is, in the very direction of the two fights the ftar would be viſible,
for an inſtant, through both; and it was the buſineſs of the obſerver to
bring the fights into this fituation; or if fixed, to note the inftant, when
it happened. Theſe fights were the invention of the noble Tycho Brahe
and, perhaps, nothing fets the ingenuity of this great man in a fuller
point of view than they did. Befide the writings, which have been men-
tioned above, Hevelius publiſhed Prodromus Aftronomia cum integro fixarum
Catalogo, deduced from diſtances taken with his large braſs ſextants and
octants.
1640 About the year 1666, or ſoon after, the Royal Obfervatory was
begun to be built at Paris; but it was not finiſhed until 1670, when the
uſe of it was affigned to M. Caffini: and in 1671 it was furniſhed with
inſtruments at a great expence. The Royal Obfervatory at Greenwich
was built in 1676, and Mr. Flamfted appointed to make uſe of it. Every
4 Y 2
one
714
BOOK 5.
ASTRONOMY
one knows to what an extent aftronomy has been carried by the obferva-
tions, that have been made here.
1641 After the death of Galileo, which happened in 1642, and indeed
prior to that time, teleſcopes were greatly improved by many ingenious
men. Fr. Fontana, a Neapolitan by birth, invented the aftronomical
teleſcope with two convex lenfes; and made one of 50 palms, with which
he faw roughneſs and fpots in the moon, the phaſes of mercury and
venus, fpots in venus and mars, jupiter's belts, faturn tricorporeum and
anfatum. Chriftian Huygens, of Zulich, in Holland, made alfo longer and
better teleſcopes, than had been done before; and particularly one of 123
feet long, which is yet preſerved in the muſeum of the Royal Society.
With theſe he conftantly, and carefully, obferved the fun, moon, and
planets, for a long time, and concluded that faturn was encompaffed with
a ring, from the various pofitions of which to the earth had ariſen all
thoſe phaſes, which fo much perplexed aftronomers. He diſcovered alſo
the fourth fatellit, which he called the moon of faturn, and wrote a
treatiſe concerning it, entitled Syftema Saturnium. He was the firft, who
applied pendulums to clocks. About the ſame time alfo Jofeph Campani,
at Rome, applied himſelf to the grinding of glaffes for long teleſcopes,
which far excelled all others, at that time. Through the munificence of
Lewis XIV. Caffini had fome made by this artiſt, of 100 and 200 palms.
Campani faw the ſhadow of ſaturn's ring upon his body, as alſo his zones,
or obfcure belts, and detected the fhadows of jupiter's fatellits in paffing
over his body. It was with one of Campani's teleſcopes that Caffini firſt
faw all the fatellits of faturn; and the Royal Academy are faid to have
had excellent teleſcope glaffes of this artist's making, which were of 200
and
300 feet focus, and that magnified four and five hundred times.
1442 About the year 1666 M. Auzout applied a micrometer to tele-
fcopes, for the purpoſe of meaſuring the diameters of the planets, and
other ſmall diſtances in the heavens; but an inftrument of this kind had
been invented many years before by Mr. Gascoigne; although it is not to
be fuppofed that this was much known abroad at that time.
1643 But notwithſtanding all theſe improvements in the conſtruction
of teleſcopes, they ftill laboured under two very obvious, and, at that
time, apparently irremovable imperfections. The firft was their great
length requifite to admit of any very confiderable magnifying power, and
the ſecond was the incorrectneſs of the image, and which was then ſup-
poſed to ariſe entirely from the aberration, cauſed by the fpherical figure
of
CHAP. II.
715
ASTRONOMY
of the lens. Perſuaded, as they were at this time, that all the imperfec-
tion of the image aroſe from the figure of the lens, and that it was utterly
impoffible to remove it, fome ingenious men turned their thoughts to-
wards fpecula; and amongſt theſe, Merfennus appears to have been the
firſt who propoſed a teleſcope of this kind in a letter to Defcartes *; but,
as it ſhould ſeem, in fo obfcure and unfatisfactory a manner, that De-
fcartes could not underſtand it; and he laboured to perſuade Merfennus
that the principle was falfe. After him, James Gregory, of Aberdeen, not
only propofed, but fhewed, how a teleſcope with ſpecula might be con-
ftructed in his Optica promota, publiſhed in 1663. But this ingenious
man, having no turn for practical mechanics, was incapable of realizing
his invention by the actual conftruction of a teleſcope. Gregory had ſhewn
that to form a perfect image of an object, the figure of the fpeculum muſt
be a parabola; but Sir Ifaac Newton, who foon after applied himſelf, not
only to improve the theory, but to perfect the mechanical part alſo, by
actually grinding fpecula himſelf, foon found that to give the great metal
fuch a figure, as the theory required, was, if not utterly impoffible, fo
extremely difficult, that he deſpaired of doing it: he therefore laid ſpecula
afide, and turned his mind towards improving and perfecting the ſcheme,
which had been propofed by Defcartes. This, as every one knows, was
to obtain a more perfect image of objects, by grinding lenſes into the
figure of one of the conic fections, inſtead of a ſphere. It was during his
purſuit of this object, that he made his ever memorable diſcovery of the
different refrangibility of the rays of light: a diſcovery which foon con-
vinced him, that the errors of teleſcopes, ariſing from the ſpherical figure
of the lens, were not fo great by fome hundreds of times as thofe, which
arofe from this property in the rays of light; and, therefore, that it would
be to no purpoſe to correct that error, while another, of fo much greater
magnitude, remained; and for which even the happy genius of Newton
could then diſcover no remedy. This circumſtance forced him to turn
his thoughts again to reflectors, and was the fortunate means of prevent-
ing the noble diſcovery of Gregory from periſhing in its infancy. This
was about the year 1668; and in 1672, Newton prefented to the Royal
Society two reflectors, which were the work of his own hands: the great
fpeculums of theſe were both ſpherical; not that he was unaware of the
fuperiority of the parabolic form, which had been propofed by Gregory;
but becauſe he thought himſelf unable to give the metals that form. He,
however, did not deſpair of its being effected by others; not, as he writes,
* Lettres de Descartes, tom. II. Nº 29. 32. 1657.
"by
1
716
BOOK 5.
ASTRONOMY
ઃઃ
by geometrical rules, but by mechanical devices," which practice and
experience in the working of them might acquire. Thus we fee, that al-
though Merfennus was the firft who thought of a reflecting teleſcope, Gre-
gory was the first who ſhewed its advantages, and how it might be made,
and Newton the firft who effected it.
1644 It has before been obferved, that when the Royal Obfervatories
of Paris and Greenwich were built they were put into the hands of Cafini
and Flamſted; men whoſe fidelity and diligence were equal to their learn-
ing; and, much to the praiſe of both nations be it ſpoken, they have ever
fince been occupied by fuch excellent men; to whofe labours we owe
many improvements in aftronomy. It was this Caffini who erected the
gnomon, and drew the famous meridian line in the church of St. Petro-
nia, at Bononia, and which, with his other labours and diſcoveries, ren-
der him worthy of immortal honour. He continued more than 40 years
at the head of the Royal Obfervatory at Paris, where he made many ob-
ſervations of the fun, moon, planets and comets, and greatly amended
the elements of their motions. His works were publiſhed by his ſon, and
fucceffor, J. James Caffini; who was afterwards fucceeded by his fon M. F.
Caffini de Thury, who very defervedly enjoys it at preſent.
1645 But by far the greateſt number of obſervations were made by Mr.
Flamsted, at Greenwich; who not only made obfervations on the fun,
moon, planets and comets, which appeared in his time, but on the fixed
ſtars alfo, of which he has given us a new catalogue, containing upwards
of 3000 ſtars, as well in latitude and longitude as in right aſcenſion and
declination: their places being rectified to the beginning of the year 1690.
Amongſt theſe are the places of many ſtars, which are ſo ſmall that they
cannot be ſeen without a teleſcope. He alfo gave us new folar tables,
and a new theory of the moon, according to Horrox. He publiſhed alſo
a very curious tract on the doctrine of the ſphere, in which he ſhewed
how to conſtruct eclipfes of the moon and fun, as well as occultations of
the fixed ſtars by the moon, geometrically: and it was upon Mr. Flam-
fied's obfervations that Halley's tables, and Newton's theory of the moon
were founded.
1646 We must not conclude this chapter without honourable mention
of that celebrated Daniſh aſtronomer, Olaus Roëmer; who by comparing
obfervations of the eclipfes of jupiter's fatellits, firſt diſcovered the pro-
greffive motion of light (§ 873); and read a differtation on that ſubject
before the members of the Royal Academy of Sciences, at Paris, Nov. 22d,
1675.
CHAP. 12.
717
ASTRONOMY
1675. In 1681 he returned to his native country, where he was made
profeſſor of aſtronomy at Copenhagen, and honoured with the title of
mathematician royal. At this place he applied himſelf to the ſtudy and
practice of aſtronomy with great fuccefs; and was the firſt aſtronomer,
who made uſe of a meridian teleſcope. Deſcriptions of all his inftru-
ments, and his valuable three days meridian obfervations of the fun,
moon, all the planets, and 80 of the principal fixed ftars, called Triduum
Roëmerianum (being the only obfervations of his, which eſcaped the fire
that burnt the obfervatory at Copenhagen in 1728) were publiſhed in a
book entitled Baſis Aſtronomia, by Peter Horrebow, one of his ſcholars,
who fucceeded him in the profeſſorſhip at Copenhagen.
CHAP. XII. THE HISTORY OF ASTRONOMY SINCE THE COMMENCEMENT
OF THE PRESENT CENTURY.
1647 About the beginning of the eighteenth century practical aftro-
nomy feemed to be almoft at a ſtand. Even the genius of Flamfted ferved
only to fhew that it had arrived at its utmoſt limits, unleſs great im-
provements could be made in the conſtruction of inftruments. It is true
Roëmer invented fome new inftruments, capable of more exactneſs than
thoſe which he found in ufe; and the genius of Dr. Hooke was turned that
way in a very peculiar manner: but notwithſtanding this, either through
the unfavourable circumſtances of the times, or through want of ſkill in
the artiſts, which they employed, nothing was done towards bringing
them into uſe, and practical aſtronomy languiſhed through want of means
to exert itself. But at the very time when this was the cafe with practi-
cal aſtronomy, the fpeculative branch of this ſcience was raiſed, at once,
to a greater degree of perfection than could have been hoped for from the
united labours of the moſt learned men, for many ages, by the amazing
genius of one man- the immortal Newton! this inimitable man pub-
liſhed his Philofophiæ naturalis principia mathematica in 1687; another en-
larged edition of it was printed in 1714, and one yet more complete in
1726. This moſt admirable work gave an entire new face to theoretical
aftronomy; the laws which Kepler, and others had felt for, as it were in
the dark, with many other laws, equally important, were here inveſti-
gated by a direct analyſis. But by a fatality which often attends great dif-
coveries, the works of this excellent man were not relifhed, for many
·
years,
718
BOOK 5.
ASTRONOMY
years, by the mathematicians and philofophers of foreign countries; who
yet adhered to the abfurd doctrines which had been broached by Descartes,
in deſpite even of the moſt rigid demonſtrations of their falfhood. True
it is, theſe things were delivered, by their illuſtrious Author, in a very
conciſe manner; and, therefore, notwithſtanding ſome celebrated mathe-
maticians, even amongſt themſelves, publiſhed, from time to time, ex-
cellent pieces of analyſis, which generally concluded in one of Newton's
propofitions; yet, as the general connection of thofe, with the other
parts of his works, was not feen, they continued blind to his excellen-
cies, which were known to, and acknowledged by his countrymen alone.
In England, however, his diſcoveries were illuftrated and explained by
divers learned men; amongſt whom were Halley, Clarke, David Gregory,'
Keil, Whifton, and many others. But that, after Newton's fyftem had, for
ſo long a time, been neglected, it fhould all at once be univerfally re-
ceived and approved of (§ 1475), is not to be attributed to chance, or
the caprice of faſhion, as fome, who are ignorant of it, are apt to think;
and from thence to expect, that fome other ſyſtem will hereafter take its
place, and bury it in oblivion. The fyftem of Newton, like that of Co-
pernicus, is ſo agreeable to the phenomena of nature, and fo well put to-
gether, that it must laft, as long as truth and reafon endure. And al-
though time may, perhaps, bring the word attraction into difufe; and
though it may no longer be thought effentially inherent in matter, yet the
laws of gravitation, as they are now called, and on which this ſyſtem is
founded, will never be forgotten.
1648 It was alſo in England, ſays M. de la Caille, that the firſt efforts
were made to render aſtronomical obfervations more perfect by the im-
provement of inſtruments; and it is thither we yet go for the moſt exqui-
fite productions of this kind. That famous mechanic, and watch-maker,
Graham, made new inftruments with an accuracy that furpriſed every one.
He alſo greatly improved the principles of watch-work, and brought
clocks to go with greater regularity than they had ever done before. The
old eight feet mural arch at Greenwich, the firſt of its kind, was made
by this excellent man, as was alſo a ſmall, but curious equatorial ſector
for making obfervations out of the meridian: but he is chiefly remarkable
for contriving the zenith ſector of 24 feet radius, and afterwards one of
12 feet, by which the aberration of the fixed ſtars was diſcovered by Dr.
Bradley (§ 848). This celebrated diſcovery was communicated to the Royal
Society, in a letter to Dr. Halley (§ 837), and printed in N° 406 of their
Z
tranfactions.
CHAP. 12.
719
ASTRONOMY
tranfactions. It fets out with relating fome curious obſervations made on
the ſtar y Draconis, begun by Mr. Molyneux, and himſelf at Kew, in 1725,
with a fector of 24 feet radius, in hopes of verifying, what had been
communicated to the public, by Dr. Hooke, concerning the parallax of
the fixed ftars. Thefe obfervations were afterwards continued by Dr.
Bradley alone at Wanfted, upon that, and other ſtars, with a ſector of
12 feet radius, which he found fully fufficient for the purpoſe; as its
fituation could be fecurely relied on to half a ſecond, when it was care-
fully adjuſted. But theſe obſervations turned out quite contrary to what
Mr. Molyneux and the Doctor expected, and to what an annual parallax
would have produced; which gave occafion to call the accuracy of Hooke's
obfervations in queſtion, and obliged Dr. Bradley to look out for ſome
other cauſe for theſe appearances. Having completed a year's obfervations,
and compared them together, he luckily conjectured that they aroſe from
the combined effects of the progreffive motion of light and the annual
motion of the earth in its orbit: and the obſervations agreed fo well with
this hypothefis, that Manfredi, who wrote againſt it, owns it could not
be accidental.
1649 In 1719 Dr. Halley, who, De la Lande fays, was without con-
tradiction the greateſt aſtronomer in England (I believe he might have
faid in the world) fucceeded Mr. Flamfted, as Royal Aftronomer, at Green-
wich. In 1676 he had been ſent by king Charles II. at the age of 21, to
the iſland of St. Helena, to obſerve the ſtars in the ſouthern hemiſphere,
and to make a catalogue of them; and he publiſhed it in 1679. In 1705
he publiſhed his Synopfis aftronomia Cometica; a work which though ſmall
in bulk, is the refult of immenfe calculation; and deferves to laſt as long
as aſtronomy itſelf. It was in this work, judging from the fimilarity of the
circumſtances attending two or three comets, which had appeared nearly
at equal intervals of time, that he ſuſpected them to be different returns of
the fame comet; and, from thence, was enabled, the firſt of any man,
to predict the return of one in 1758, or 1759 (§ 1301). Halley publiſhed
many learned differtations in the tranſactions of the Royal Society, parti-
cularly that relating to the ufe which might be made of the tranfit of the
planet venus over the fun's difk, if it be carefully obſerved in proper
places. He appears alfo to have been the first who difcovered the accele-
ration of the moon (§ 1075), and gave a very ingenious method of de-
termining her parallax from three obferved phaſes of a folar eclipfe. He
compoſed tables of the fun, moon, and all the planets; and, in the firſt
nine
4
Z
720
BOOK 5.
ASTRONOMY
nine years of his being at Greenwich, made near 1500 obfervations of the
moon; all which he compared with the tables, and noted the differences,
which he thought would return in the fame order, after a period of
about 18 years. He continued theſe obſervations with great diligence till
within a few months of his death, which happened on the 14th of Ja-
nuary 1742.
1650 During the period that Halley was at Greenwich aftronomy was
not altogether neglected abroad. The attempt which was made in France
to meaſure a degree upon the earth gave rife to a very warm difpute con-
cerning the figure of it. Cafini, from Picart's meaſure, concluded that
the earth was an oblong ſpheroid: Newton from a confideration of its
diurnal rotation, and the laws of gravitation, had fhewn that it was an
oblate one, flatted at the poles. To determine this curious point, with
certainty, by actual menfuration, Lewis XV. K. of France, refolved to
have two degrees of the meridian meaſured, one under, or very near to
the equinoctial, and the other as near as poffible to the north pole. To
perform the latter, the Royal Academy of Sciences at Paris made choice
of M. M. De Maupertuis, Clairaut, Camus, and le Monier, members of
the Academy; and M. the Abbé Outhier, a correfpondent of the fame Aca-
demy. Theſe were joined by M. Celfius, profeffor of aftronomy at Upfal:
they ſet out from France in the ſpring of the year 1736, and returned in
the autumn of 1737; having performed the buſineſs of their miffion in a
manner that was fatisfactory to all Europe (§ 1192). For the fouthern
expedition M. M. Godin, De la Condamine and Bouguer were felected, and
to them the King of Spain joined Don George Juan, and Don Anthony de
Ulloa, two very ingenious gentlemen, and officers of the marine. They
left Europe in the fummer of the year 1735; and, after meeting with in-
numerable hardſhips, dangers, and delays, from the nature of the coun-
try, and the circumſtances of the times, finiſhed their obſervations, and
returned to Europe, by different ways, and at various times, in the years
1744, 1745 and 1746. The refult of this arduous undertaking is now
well known. Newton's inveſtigation was confirmed, by experiment, in
the completeſt manner poffible, and Picart's meaſure was reviſed by Cafini
and De la Caille, and his errors corrected; after which it was found to
agree very well with the other two. While M. M. Bouguer and de la Con-
damine were in Peru on this occafion, it occurred to them that the New-
tonian theory of attraction might be put to the teſt alſo, by obſerving the
effect, which fome of the largeſt of the cordilleras had on the plumb-line
of.
CHAP. 12.
721
ASTRONOMY
of one of their largeſt inſtruments (§ 1200), and which, on trial, turned
out to be about 7 or 8 feconds of a degree: but the experiment appears
not to have been made in the moſt fatisfactory manner *
1651 The reflecting teleſcope, which had been invented by Gregory,
and executed by Newton, was greatly improved by Mr. Hadley, and a very
complete and powerful inftrument, of this kind, was prefented to the
Royal Society, by him, in 1719. The fame gentleman has rendered his
memory immortal by the invention of the reflecting quadrant, which he
preſented to the fame fociety in 1731, and which is now in univerſal uſe
at fea; and, without which, all improvements of the lunar theory would
have been uſeleſs for determining the longitude, through the want of an
inftrument proper to make the obſervations with. It, however, appears
that an inſtrument, exactly fimilar to this in its principles, had been in-
vented by Sir Ifaac Newton, and a deſcription of it, together with a draw-
ing, given to Dr. Halley, by the inventor, when he was preparing for his
voyage to obſerve the variation of the needle in 1701.
1652 On the death of Halley, in 1742, he was fucceeded at the Royal
Obfervatory by the Rev. Dr. Bradley; who, if he was inferior to Halley
in the powers of mathematical inveſtigation, greatly exceeded him in the
practice of aſtronomical obfervations. Bradley was the first who made
obfervations capable of detecting the leffer inequalities in the motions of
the planets, and fixed ftars. He had already diſcovered, and fully ex-
plained the aberration of the fixed ſtars, and the nutation of the earth's
axis; and he now applied himſelf, with the utmoſt affiduity, to the per-
fecting of the lunar tables. He alſo obſerved the places, and computed
the elements of the comets, which appeared in the years 1723, 1736, 1743,
and 1757, which are printed in the philofophical tranfactions. He made
new and elaborate tables of the motions of jupiter's fatellits, from his own
obfervations and thoſe of Dr. Pound, which are added to the tables of
Halley. He was not only an accurate but an unwearied obferver of the
fun, moon, planets, and fixed ftars; and from the multitude and accu-
racy
of theſe obfervations he was enabled not only to give the moſt accu-
rate table of the mean refractions, yet extant, but also to give moſt ex-
* In the fection here referred to, the manner in which M. Bouguer made this obfervation, was
miſunderſtood, at the time when it was written. One of the ftations was on the fouth fide of the
mountain, nearly in the plane of the meridian, which paffed through its center of gravity, and the
other almoſt in the fame parallel of latitude, but about à league and half to the weftward; fo that the
effect of attraction, in the direction of the meridian, became exceeding ſmall, in compariſon of what
it was in the former fituation.
4 Z 2
cellent
722
ASTRONOMY
BOOK 5.
cellent rules for computing the variations of thofe refractions, arifing
from different ſtates of the air, as indicated by the barometer and ther-
mometer.
1653 In the year 1750 he procured a very large tranfit inftrument to
be made for the Royal Obfervatory, by Mr. Bird, inſtead of the ſmall one
which had been uſed by Halley, and alſo a new mural quadrant, of braſs,
which is of eight feet radius. With theſe inſtruments he began to make
obſervations on the heavenly bodies with redoubled ſpirit and induſtry; ſo
that between this time and his death, which happened on the 13th of
July, 1762, he made obſervations for fetting the places of all the ſtars in
the Britiſh catalogue, together with near 1500 places of the moon; much
the greater part of which he compared with the tables of Mr. Mayer.
1654 Between the years 1740 and 1750, the theory of the moon,
which had been given long before, by our illuſtrious countryman Newton,
in a general way, began to be confidered by many eminent mathemati-
cians: in particular by M. M. Clairaut, D'Alembert, Euler, Mayer, Simpson
and Walmsley. But amongſt theſe, none diftinguiſhed themſelves in fo
eminent a degree as thofe celebrated men Clairaut, Euler and Mayer; and
if the two former have, in fome reſpects, fhewn greater depth of ma-
thematical knowledge, the laſt has been much more happy, than they
were, in a fkilful arrangement of his tables, for the eaſe and expedition
of computation. In confequence of theſe exertions, M. Euler publiſhed
his lunar tables in the Almanac Aftronomique, printed at Berlin, for the
year 1750. M. Clairaut's tables came out in 1752, in anſwer to the prize
queftion, which had been propofed by the Imperial Academy of Sciences
at Peterſburg, in 1750: and Mayer publiſhed his in the Gottingen Acts for
1753; in which he excelled both the former, not only in eaſe and ele-
gance of computation, but in exactneſs likewife: -owing, perhaps, in
fome meaſure, to the judicious ufe which he made of a number of Dr.
Bradley's obfervations, fent by Mr. Gael Morris to M. Euler, and given
by him to M. Mayer. In theſe tables, the errors in longitude never ex-
ceeded two minutes: and, having yet farther improved them, he ſent a
copy to the lords commiffioners of the Britiſh Admiralty, in 1755; and
it was this copy which Dr. Bradley compared with his obfervations, as
mentioned in the preceding article. His laft corrections of them were
afterwards remitted over by his widow, for which ſhe, and her child-
ren, received a reward from the commiffioners of longitude of 30001.
fterling.
1655 While
CHAP. 12.
723
ASTRONOMY
1655 While fo many learned men were employed on the lunar tables,
thoſe of the fatellits of jupiter were not neglected. Befide what was done
in England by Mr. Pound and Dr. Bradley, which has been mentioned
above, M. Wargentin, a moft excellent aftronomer of Sweden, publiſhed
a ſet of tables for computing the times of the eclipſes of theſe fatellits in
the Upſal Acts, for 1741; and the fame ingenious gentleman has fince
given us emendations of them, at different times, which far exceed any
thing that had been done, on this head, before.
1656 The conſtructing and dividing of large aftronomical inftruments
was alſo, about this period, carried, perhaps, to the utmoſt degree of
perfection, they will admit of, by Mr. John Bird, a moſt excellent artiſt;
and whofe labours are the ornament and moſt valuable furniture of the
capital obfervatories in Europe. Reflecting teleſcopes were brought to
great perfection by Mr. James Short. This ingenious artift was alfo the
firſt who executed the divided-object-glaſs micrometer: it had been thought
of by M. Louville, and feveral other perfons long before; and a deſcription
of one, agreeing nearly with Mr. Short's inſtrument, had been given by the
late ingenious Mr. Dollond, in the Philofophical Tranſactions for 1753;
but if it had not been for the great ingenuity and ſkill of Mr. Short, in
figuring and centering glaffes of this kind, it is highly probable the thing
might yet have remained, as it was, -an ingenious thought, without be-
ing ever brought into practice.
1657 From the time that Mr. Hadley had found means to conſtruct re-
flecting teleſcopes, both on the principles of Gregory and Newton, with fo
much perfection, refracting teleſcopes had been finking gradually into
difufe, and would, in all probability, foon have been totally laid afide by
aftronomers. The notion which had been entertained, even by Sir Ifaac
Newton himſelf, that the divergency of the rays of light, ariſing from the
difference of their refrangibility, was always proportional to the refract-
ing power of the medium, had become fo generally received by opticians,
that no attempts were made to improve refracting teleſcopes before the
late ingenious Mr. John Dollond, who has been mentioned above, took
them in hand. This able optician in the courfe of many optical experi-
ments, diſcovered that, contrary to the general opinion, the refractions
of two priſms, if made of different kinds of glaſs, might be equal, and
yet the divergency of the rays, arifing from the difference of their refran-
gibility, might be very confiderable. This led him to conclude that there
might be equal divergency with different degrees of refraction; and if ſo,
that
724
BOOK 5.
A
RONOM *
that refraction might oduced without co... Subfequent experi-
ments fully proved the tuch of this fuppofition: and from this principle,
he has found means to conftruct refracting teleſcopes which are fuperior
to any reflectors of the fame lengtn.
1658 Many important improvements were made to the fcience of aftro-
nomy in France by the two Caffinis, and James Philip Marald; who was ne-
phew to the father, and many years a worthy colleague with the fon, in the
Royal Obfervatory at Paris. We find many of their works diſperſed in the
Memoirs of the Royal Academy of Sciences. Befide theſe, and others, who have
been before mentioned, France produced many very learned men, who
cultivated and improved the ſcience of aftronomy; amongſt whom it would
be unjust not to diftinguish the induftrious, the accurate, and faithful
Lewis de la Caille, to whom we are indebted for a moft excellent fſet of
folar tables, in which he has made allowances for the attractions of jupi-
ter, venus, and the moon. In 1750 this excellent aftronomer went to
the Cape of Good Hope to make obfervations, in confort with moſt of
the celebrated aſtronomers in Europe, for determining the moon's hori-
zontal parallax, as well as that of the planet mars; and from thence that
of the fun alfo. From theſe obſervations it appeared that the ſolar
rallax could not greatly exceed 10". While he was here, he re-examined
and adjuſted the places of the ſouthern ſtars, with great accuracy; and
meaſured a degree of the meridian at that place. In Italy aftronomy was
cultivated with great affiduity by Signor Bianchini and Father Bofcowich at
Rome; Euftachius Manfredi and Profeſſor Zanotti at Bologna; Father Frifi
at Milan, and many others. Sweden produced, befide M. Wargenten, M.
M. Klingenstern, Mallet and Planman. In Germany, the celebrated Euler
and Mayer fhone like ftars of the firſt magnitude, attended by the younger
Euler, M. M. Lambert, C. Mayer, Grifchow, Father Hell, at Vienna, and
many more.
pa-
Such was the ſtate of aſtronomy about the beginning of the year 1760,
when all the learned focieties in Europe began to prepare for obferving
the tranfit of the planet venus over the fun's diſk, in the following year;
which our learned countryman, Dr. Edmund Halley, with immortal repu-
tation to himſelf (§ 1357), had foretold more than eighty years before it
happened; and at the fame time had fhewn, what an important uſe aftro-
nomers might make of it. Unfortunately for the caufe of fcience, many
of the aſtronomers, who were ſent out to obſerve this fingular phenome-
non, were prevented by unavoidable and unforeſeen accidents from reach-
ing
CHAP. 12.
725
ASTRONOM Y
ing thofe places, which were moſt proper for the purpofe; and others
were diſappointed by the badneſs of the weather. It moreover happened
that the circumftances of the phenomenon were much leſs advantageous
for the purpoſe of determining the fun's parallax, than had been expected
by Dr. Halley, owing to the faults of the tables, which he made ufe of;
ſo that notwithſtanding there was reafon to believe the parallax of the
fun, deduced from the obſervations of this tranfit, was very near the truth,
yet aſtronomers were left ſomewhat in ſuſpenſe, and to hope for a more
fatisfactory account of it from the obfervations of that which was to hap-
pen in 1769 (§ 1360 & 1361).
Upon the death of Dr. Bradley, in 1762, he was fucceeded in his pro-
fefforſhip at Oxford by the Rev. Mr. Hornsby, a young man, but a very
ingenious aftronomer; and at the Royal Obfervatory by the Rev. Mr.
Bliss, Savillian Profeſſor of Aſtronomy at Oxford, who being in a declin-
ing ſtate of health, when he was appointed, lived to hold the obſervatory
but a very
little time; and was fucceeded by the learned and indefatigable
Nevil Maskeline, D. D. the preſent Aftronomer Royal, whofe memory will
be rendered immortal by his affiduity and fuccefs in bringing the lunar
method of determining the longitude at ſea into general practice.
*
I ſhall here cloſe the hiſtory of aſtronomy; the moſt delightful, the
moſt extenſive, and the fublimeft fcience which the great Author of Nature
has held forth for employment to the faculties of man: the ſtudy of
which, perhaps, firſt led mankind to the true knowledge of his great
and allwife creator. For although a
For although a tradition, ſpread through all na-
tions, from the firſt ages of the world, teaches us that all beings owe
their birth to the operation of God, and that nothing, which exiſts, has in
itſelf the power of exifting, independently of the influence of that Su-
preme Being; yet fome of the ancients have faid that the univerſe is full
of different divinities, which manifeft themſelves under fenfible images to
our eyes, our ears, and all our organs of fenfe: but if this notion of the
Deity makes it fomething eaſier to explain the effects of the power of
God, it does not at all agree with his nature. God is really the maker
and preferver of all things; but we muſt not have the fame conceptions
of him as of a mortal artiſt. He operates inftantaneouſly, without pre-
meditation, inſtruments or affiſtance of any kind. The multitude and
* Expofition du fentiment d'Ariftote fur le méchanifme. général de l'univers, et fur la nature de
fon auteur. Memoires de Trevoux, aout 1761.
variety
726
BOOK 5.
ASTRONOMY
variety of his works give him no embarraffment or wearinefs: endowed
with a power irreſiſtible, and unlimited, he operates at all times, and in
all places, over all kinds of matter, and of whatever form, with equal
facility and efficacy.
But notwithſtanding the power of God is manifeſted in all his works,
it is in the heavens that it beams forth in its greateſt luftre. He has
choſen his refidence in the moſt elevated region, and therefore we call
him The Most High. From thence the energy of his action is propagated
with gradual diminution down to the loweſt place, the earth, which we
inhabit. From thence he directs the courſes of the planets, determines
the circumſtances of their motions, and fixes the times of their revolu-
tions. As a general at the head of an army, he gives the fignal to the
heavenly bodies, and immediately they ſhoot forth through immenſe
ſpace, and follow the tracks which he has marked out for them: fome-
times fhewing themſelves to us, and fometimes diſappearing, on account
of the great variety of their motions and phaſes. It is in confequence of
the laws laid down by him that the moon goes round the earth in a month;
the fun, mercury and venus in a year*; mars in two years; jupiter in
twelve; and faturn in thirty. It is he that has combined together the two
motions of the fun, one from east to west, which conftitutes the regular
viciffitudes of day and night; and the other, his declining from fouth to
north and from north to fouth, by which means the ſeaſons of the year
are brought about. He it is, who, at the appointed times, fends falutary
winds, and fruitful rains and dews; who gathers together the waters in
their fources, and caufes them to flow from thence in the beds of rivers
to their great receptacle, the fea. It is he who makes the buds to open,
the fruits to ripen, and animals to be prolific: in fine, it is he who orders
all beings according to their different natures, and regulates the viciffi-
tudes of their birth, their growth and diffolution, which conftitute the
whole of their duration. But what chiefly deſerves our admiration is,
that this multitude of effects, whether alike or different, is produced by
the moſt fimple means: thoſe bodies neareſt to the Deity receive their
* It appears from this paffage that Aristotle had embraced that fyftem of the world, which is by
fome afcribed to Martianus Capella, and by others, to the ancient Egyptians: but as Ariſtotle lived be-
fore Capella, it is evident from hence he was not the inventor of it.
It is eafy to fee that the expreffion here is not accurate. As God is every where equally prefent,
all bodies are equally near to him. But according to the doctrine of Ariſtotle God is not every where
actually prefent, in his real effence, but only by the exercife of his power. See the note upon this
paffage. Mem. de Trevoux.
1
motion
CHAP. 12.
727
ASTRONOMY
motion immediately from him and communicate it to thofe which are
contiguous; thofe fucceffively to others, until it goes through all nature.
Motion therefore is fimple and uniform; and the various kinds of it,
which we obſerve, are caufed by the different forms or affections of the
bodies which receive it. Thus, throw a globe, a cube, a cone, and a
cylinder out of a veffel at the fame time, and you will fee theſe four folids,
though incited by the fame impulſe, take different motions, according to
the diverfity of their figures, and their poſitions when they iffued out of
it. Here we fee, in miniature, a repreſentation of what nature exhibits
in the great. All its parts are put in motion by one and the fame im-
pulfe, but this force is differently modified, according to the different
diſtances and peculiar qualities of each body: and from hence arifes the
variety which is obfervable in the direction and velocity of different bodies;
but eſpecially in thoſe which we fee in the heavens.
For the reft, if the author of fo many wonders is to us inviſible, we
are not, on that account, to deny his power, or his exiſtence. I cannot
ſee my own foul, and yet the effects it produces in me, and around me
are fenfible proofs of its exiſtence: in like manner God, inviſible in him-
felf, is viſible in all his works; and in them appears equally ſtrong in
power, admirable in wiſdom, eternal in duration, fupreme in perfection,
and free from all pollution: he inhabits a place illuminated by everlaſting
light; and, being himſelf immoveable, moves all nature at his pleaſure.
As we ſee in great cities that the law, always fixed and invariable in itſelf,
directs and produces the vaſt variety of employments of the citizens, and
turns them a thouſand different ways with reſpect to the different condi-
tions, apprehenfions and fentiments of each of them, fo in the vaſt city
of the univerſe, God, who is the first, the moſt equitable, and moft per-
fect of all laws, cauſes all the changes which happen, himſelf not ſubject
to change.
given to him, taken
He is called Him by
He is faid to be
God is really one; but different names have been
from his different operations and relations to us.
whom all live, becauſe it is he who animates every thing.
the Son of Time, becauſe his duration extends from ages without begin-
ning, to ages without end. They call him the Thunderer, the Sender of
Lightening, the Giver of Rain, the Director of Harvest, the Guardian of
Towns, the National, the Social, the Hofpitable, the Victorious, the Expia-
tor, the Avenger, the Saviour, the Deliverer, the Celestial, the Terrestrial:
in ſhort, he has as many names as there are beings or events; becauſe
there
5 A
728
BOOK 5.
ASTRONOM Y.
there is nothing in the univerſe whereof he is not the firſt caufe. It is
he, whom we worſhip under the name of Fate, or Neceffity, becauſe he
diſpoſes, according to his pleaſure, the deſtinies of this world. He ties
together, by infallible laws, that chain of cauſes and effects, which we
fee inceffantly fucceed one another, with fuch regularity, and without
intermiffion. Fortune is only God, confidered as the diſtributor of good
and evil. The fable of the three fifters, Parca, of which one prefides
over time paſt, another over the preſent, and the third over the time
which is to come, is only an emblem of God's fovereign dominion over
all ages. In fine, God, to make uſe of a very ancient faying, holds in
his hands the beginning, the middle and the end of all things, and leads
them every one to their proper end by direct and certain ways; juftice
follows him, ready to puniſh the breach of his laws: he, and he only, is
happy, who, after the example of the Deity, never forfakes that in-
eftimable virtue. Without this virtue true happineſs is never to be
found.
THE EN D
IN
ADVERTISEMENT.
N the year 1764, Dr. Long publiſhed the third book of his Aſtronomy,
as a part only of his fecond volume. Before the time of his death he
had finiſhed and printed off the fourth, and a ſmall part of the fifth
book, viz. the three firft chapters of it, and the beginning of the fourth,
including p. 654. He had indeed printed off the leaf following, which,
it was thought proper, ſhould be cancelled, and the new part begins
p. 655. A few hints only were left in the Author's own handwriting to-
wards finiſhing the remainder, which may, now and then, be perceived
in the courſe of the Work. One inſtance of this kind occurs p. 663, re-
lating to a converfation which he had held with the old Lord Pembroke.
A fhort time before he died, he had defired Mr. Dunthorn, whom he no-
minated one of his executors, to finifh the Work. Mr. Dunthorn made
indeed a rough draught of the remaining part of it; but being much en-
gaged in public buſineſs, by his being appointed fuperintendant of the
works of the Bedford Level Corporation, his avocations became great and
unavoidable, and he left it at laſt in a very imperfect ftate. After his
death, Mr. Wales, F. R. S. Maſter of the Royal Mathematical School in
Chriſt-Hoſpital, and Editor of the Original Obſervations, made by him-
felf and others in the courſe of a voyage round the world, was prevailed
upon to reviſe and correct Mr. Dunthorn's continuation, and to complete
it upon the original plan, ſketched out and begun by the Author himſelf,
in that part of the fifth book which had been printed before he died: and
it is owing to the care of Mr. Wales that it is now preſented to the Public
in its preſent ſtate. It must be further obferved, that the Rev. Dr.
Maſkelyne, Aftronomer Royal, out of his eſteem for the late Author of
this Work, hath been pleaſed to pay a kind attention to it. In the
fourth book, particularly in the ſheet 4 M, a leaf or two hath been can-
celled by his advice, and hath been replaced with ſome material improve-
ments. The Work. concludes with the opinion of Ariftotle, concerning
5 A 2
the
ADVERTISEMENT.
the general mechaniſm of the World, and the nature of the Maker there-
of, as it is inferted in the Memoires de Trevoux for Aug. 1761. Our
Author himſelf had intended it for the conclufion of his Work, and had
tranſlated it from thoſe Memoires with that view, and the continuator
hath found it neceffary to make therein but very few alterations. The
paffage itſelf from whence it is taken is curious, and will repay the Reader
for any trouble he ſhall take in comparing the extract with the original,
which is to be found in the two laſt chapters of Ariſtotle's Treatiſe con-
cerning the World.
Our Author was born Feb. 2d, 1680, O. S. in the parish of St. Peter,
Thetford, in the county of Norfolk, at a place called Croxton Park. He
was educated at the Public School in Norwich, and was admitted into
Pembroke Hall March 4, 1696. He took the degrees of Bachelor and
Maſter of Arts at the ufual times after his admiffion. He was elected
Fellow of the College March 6, 1703. At the public Commencement
celebrated at Cambridge 1714, he was appointed to fpeak the Mufic
Speech, which was then publiſhed, and reprinted 1730.
In the year 1716, he was inftituted to the Rectory of Overton Water-
ville, in the county of Huntingdon, upon the preſentation of the College,
and in the year following he refigned his Fellowſhip, by a letter dated
Dec. 24, 1717, from Market Boſworth, in Leiceſterſhire, in which year
he had been entered as Fellow-Commoner at Emanuel College, where he
refided for fome time as private Tutor to Sir Wolftan Dixie.
He afterwards returned to Pembroke Hall, and read public Lectures
there in Aſtronomy, which he continued for many years of his life.
In the year 1728, he proceeded to take the degree of Doctor in Divi-
nity, and on the Commencement Sunday he preached before the Univer-
fity, on the Bleffedneſs of Believing, from John xx. 29. and publiſhed
his Sermon at the requeſt of the Vicechancellor, and other Heads of
Colleges.
In the year 1731, he publiſhed The Rights of Churches and Colleges
defended, in anſwer to a Pamphlet by Everard Fleetwood, Efq; with Re-
marks on fome other Pieces upon the fame Subject. This Treatife came
out under the name of Dicaiophilus Cantabrigienfis.
Oct. 12, 1733, he was elected Maſter of the College, upon the refig-
nation of Dr. John Hawkins, of Pennans in Cornwall, and in the month
following he was chofen Vicechancellor of the Univerſity.
March
ADVERTISEMENT.
March 16, 1749, he was elected Lowndes's Aftronomical and Geome-
trical Profeſſor in the Univerſity of Cambridge, and was the firſt Profeſſor
upon that foundation *.
In the year 1751, he vacated the Rectory of Overton Waterville by
ceffion, having obtained the Rectory of Bradwell, near the fea, upon the
preſentation of Thomas Hawkins of Trewithen, in the county of Corn-
wall, Efq; a near relation of the late Dr. Hawkins, his immediate Prede-
ceffor in the Maſterſhip.
In the year 1757, he publiſhed an edition of Profeffor Oakley's Hiſtory
of the Saracens; to which he prefixed an Account of the Arabians or Sa-
racens, of the Life of Mahomet, and of the Mahometan Religion. It
appears that he employed himſelf in this Work upon a principle of bene-
ficence. For it is ſaid, in the title-page, to be printed for the fole benefit
of Mrs. Ann Oakley, by permiffion of Henry Lintot, Efq; who had pro-
bably the copyright of the Profeffor's Hiftory. She was daughter of the
Profeffor, and is ſtill living.
Our Author died Dec. 16, 1770, having nearly completed his nine-
tieth year.
*The electors were at that time Philip Lord Hardwicke, Lord Chancellor; Lionel Duke
of Dorſet, Lord Prefident of his Majeſty's Privy Council; John Earl Gower, Lord Privy Seal;
Charles Duke of Marlborough, Lord Steward of his Majefty's Houfhold; and Henry Pelham,
Efq. Firſt Lord Commiffioner of the Treaſury.
Pembroke Hall,
June, 1784.
ÉR RATA.
In feveral places for Antidiluvians read Antediluvians. page 495. line ult. (in Vol. II.)dele
one on the north, the other p. 496. 1. 2. for 14″. r. 7". or 8". fee p. 721. p. 562. l. 5. dele day.
p. 588. 1. 22. for etherial r. ethereal. p. 596. 1. 32. infert and which. p. 607. laft line but one,
for 142. r. 1412. p. 608. l. 7. & 9. for though r. through. p. 613. l. 2. for cirles r. circles. p.
620. 1. 6. for awkard r. awkward. p. 636. 1. 29. for 18'. r. 18″. p. 643. l. ult. r. confequence.
p. 644. 1. 5. r. language. 1. 24. & 34. for Hugens r. Huygens. p. 649. l. 14. for hight r. height.
p. 674. 7. 18. r. philofophers. p. 682. l. 30. for ſhews r. fhew. p. 684. 1. 5. for has r. have. p.
686. 1. 4. after firſt infert of thoſe. p. 702. 1. ult. the catchword (frequently) not carried up to
P. 703. p. 711. laſt line but two for 1739. r. 1639. p. 718. l. 15. for 1475. r. 1476.
THE
CONTENTS OF VOL. II.
BOOK III.
Chap. 1. Of the fecondary planets: the
moon's motion, 357•
The earth, jupiter, and faturn, attended by
fecondary planets, 357. The earth by
the moon, ib. Its diftance from the
earth, ib. A periodical month, ib.
Orbit of the moon, and of the fatellits of
jupiter and faturn, ib. Probability that
venus has a fatellit, 357. Obferved by
Mr. Caffini, 358.—By Mr. Short, ib.
The moon's apparent orbit, 359.
The
The orbit of every ſecondary planet an el-
lipfis, ib. The line of the moon's ap-
fides, ib.- Perigee or lower apfis what,
apogee or higher apfis what, ib. Mean
diſtance, ib.
diftance, ib.
orbit, ib.
The
Line of the moon's mean
Excentricity of the moon's
Mean excentricity of the
moon's orbit how much, 360. The
orbits of the fatellits of jupiter and faturn
nearly circular, ib. The motion of every
fecondary planet not equable, ib.
planes of the orbits of the fecondary planets
inclined to the planes of the orbits of their
primary, ib.
Inclination of the plane of
the moon's orbit how much, ib. The
moon's nodes, 361. Afcending node,
called the dragon's head, ib. Defcend-
ing node, called the dragon's tail, ib.
The line of the moon's nodes, ib.
North and fouth limits, ib. The moon
in conjunction, oppofition, quadrature, 362.
Syzygies, line of fyzygies, what, ib.
Synodical month, or lunation, ib.
Increafe and waining of the moon, ib.
A new moon, a crefcent, half moon, gib-
bous, a full moon, called phaſes of the
moon, ib.
The moon's motion, or her
e
How
elongation from the fun, 363.
much in a day, ib.- Appulfe of the moon
to a ſtar, ib.
Occultation what, ib.-
The progreffion of the moon's apogee, 364.
The regreffion of the moon's nodes,
365.
Chap. 2. That the fecondary planets are
opake bodies, and borrow all their
light from the fun, 365.
The moon an opake body of a rough ſurface,
366. When he appears a new, and
when a full moon, 367.— Her dichoto-
my, ib. The fatellits of jupiter and fa-
turn go through all the phaſes of the moon,
368.
Chap. 3. Of eclipses of the moon, 369.
Eclipfe what, 370. The Chineſe ancient
obfervers of eclipfes, ib. Eſpecially of
the fun, ib. Diſtance of the moon from
the earth known from her horizontal paral-
lax, 371.
How found by Ptolemy, ib.
Moon's greateft latitude what, ib.
Horizontal parallax how found by Keil, ib.
Moon's diſtance from us variable, 372.
Tables of the parallax of the moon,
and of her diftance made for every 5º of
her anomaly, ib. Another variation in
the diftance of the moon arifing from the
fituation of the earth and moon in respect of
the fun, ib. How ſtated by Newton, ib.
ſtates the mean diſtance of
How he
the moon, ib.
moon, 373.
moon, ib.
The true diameter of the
Superficial content of the
Solid content of the moon,
ib. Shape of her fhadow, and of the
fhadows of the other planets, a cone, ib.
The moon not eclipfed by the fhadow
of
CONTENT
S.
of the earth alone, ib.
of the atmoſphere, ib: -
Of the fhadow
Of the height of
the fhadow, called alfo its axis, 374
Moon eclipsed by the ſhadow of the atmof-
phere, 375. Shadow of every planet
encompaffed with a penumbra, ib. Of
the shape calathoeides, ib. Circle of the
earth's (hadow what, 376.Difks of the
fun, earth, and moon, 377. Digits and
fcruples what, ib. The quantity of a
lunar eclipſe, 378. Duration of a lunar
eclipfe, ib. The limit of a lunar eclipfe,
379. When there will be no eclipfe, ib.
A partial eclipſe, ib. An eclipse
total without ſtay, 380.- An eclipſe total
with ftay, ib. The fuppofed fhadow of
the earth, 381.- Its axis, ib. The
ſhadow of the atmoſphere, ib. The true
fhadow of the earth, ib. Its height, ib.
To find the angle of the cone of the
fuppofed thadow, ib. To find the axis.
of the cone of the fuppofed fhadow, 382.
To find the angle and axis of the cone
of the (hadow of the atmoſphere, ib.
To find the angle of the true fhadow of the
earth, 383. To find the height of the
true ſhadow of the earth, 384. To find
the diameter of the circle of the earth's tha-
dow, 385. A fecond method, ib.
To find the fun's distance from the earth,
ib. - A third method of finding the femi-
diameter of the circle of the earth's fhadow,
by Kepler, 386. Apparent diameter of
the moon found, ib.To find the greateſt
limit of lunar eclipfes, 387. To find the
leaft limit of lunar eclipfes, ib. Argu-
ment of the moon's latitude what, ib.
The mean anomaly of the moon, ib.
The true anomaly of the moon, ib.
Table of the moon's latitude how framed,
388. Her parallax and femidiameter
made for every 5th or 6th degree of her
anomaly, ib. Difference of the apparent
diameter of the moon in different altitudes,
ib.- The way of the difk of the moon
through the circle of the earth's ſhade, ib.
•
Chap. 4. Of eclipfes of the fun, 389.
Eclipfe of the fun total, 390. Central, ib.
Partial, ib.- The quantity of a fo-
lar eclipfe in general, 391. The quan-
tity of a folar eclipfe in any place determin-
ed, ib. -Eclipfe barely total, ib. --
More than total, ib. annular, ib,
The quantity of a folar eclipfe in any place
eftimated by digits, ib. Shape of the
moon's fhadow projected on the earth, ib.
Largeness of the moon's fhade pro-
jected upon the earth, 392. Of annular
eclipfes, ib. The way of the moon's
ſhadow upon the earth, how determined,
393. Eclipfes of the fun confidered two
ways, ib. Pofition of the culps, 394.
The time of the middle of the eclipfe,
395. The largenefs of the earth's diſk,
how found, ib. Duration of folar eclip-
fes, 396. Beginning of general eclipfe,
A central eclipfe of the fun total,
with or without ftay, 397. Velocity of
the moon's fhadow, ib. Duration of
total darkneſs, ib. Eclipfe of the fun,
how it appears in the Heaven, 398.-
Apparent diameter of the moon in ſyzygy,
400. The moon in the zenith larger
than in the horizon, ib. Apparent mo-
tion of the moon, fwifteft in zenith, 40.
ib.
—
Duration of a central, folar eclipſe, 402.
Duration feen from the furface of the
earth, ib. Darknefs in a total eclipfe,
how diminished, 403. Moon's atmof-
phere, 404. Total eclipfes defcribed,
ib. &c. Moon's atmoſphere, proofs of
one, 405, &c. - Duration of total dark-
nefs in a central eclipfe, 410. Limits of
folar eclipfes, 411. A table of the
moon's femidiameter, horizontal parallaxes,
and hourly motion, 412. Of the moon's
parallax, 413. Circle of pale light round
the moon, in a folar eclipfe, 415. At-
moſphere of the moon; other proofs of it,
416.
Chap. 5. The frequency of eclipfes:
their reftitution: their uſes, 417.
Mean motion of the moon, 421. Epochs,
and their ufe, 422. Úles of ecliples in
geography, ib.in chronology, 423.
To find the moon's true place by a lunar
eclipfe, ib. To find the mean motion
of the moon, ib.
To determine an
epoch of the moon's mean motion; the
place of her apogee, and her firft inequality,
426. To find the motion of the moon's
apogee, 428. The place of the moon's
nodes, 431.
Moon's motion acçelerat-
ed, 433.
Chap.
CONTENT S.
Chap. 6. The harvest moon: the bori-
zontal moon, 436.
Harvest moon, 436. Beſt harvest moon,
441. Horizontal moon largeſt, 442.
Solutions, ib. — Of the figure of the fky,
444. The blue ſky, a ſmall ſegment of
a ſphere, 445.
motion, ſtrait lines, or eliptical, 476.
What ſpots are, 478.- Opinions about
the fun, 479. Sun's atmoſphere, ib.
Semita luminofa, or zodiacal light, 480.
Chap. 10. Belts and ſpots upon the pri-
mary planets: their rotation round
their own axes: their shapes, 482.
Chap. 7. The moons or fatellits of ju- Belts and ſpots upon the primary planets, 482.
piter, 447.
Their ufe for longitude, 448.
Tables of
their motion, made by aftronomers, 449.
Their periodic times, ib. Their
apparent motion direct, retrograde, in ftrait
lines, or ellipfes, 450. Their orbits el-
liptical, 451. Occultation of them, ib.
The fhadow of them feen upon their
primary, 452.Entrance into, and exits
out of the thadow of jupiter, 453.-Du-
ration of their eclipfes, 454. Inclina-
tion of their orbits, ib. Inequality of
their motions, 455.- Progrefs of light,
ib.
Stars not in the places where
feen by us, 456.. Eclipfes of fatellits
diſcover longitudes, 457.- Cautions to
be obſerved about the length of teleſcopes,
ib. May be obferved at fea in calm
weather, 459.—Longitude by a watch,
460. Magnitude of the fatellits, 461.
Elements of eclipfes of jupiter and ſatellits,
462. Diameters of their orbits, how
found, 463.
Chap. 8. The ring of faturn: his moons
or fatellits, 464.
The anfæ thereof, 466. His five moons,
Their periodic times, ib.
468.
All
nearly in the fame plane, except the 5th, ib.
Inclination of their orbits, 469.
Spots in the 5th ſatellit, 470. His
belts, ib.
Chap. 9. Spots in the fun: the rotation
of the fun round his own axis: the
fun's atmoſphere, 470.
Spots in the fun, ib. Of various fizes,
471. And fhapes, 472. Number
various, ib. Rotation of the fun, 473.
How found, 475.-The fun's equa-
tor, ib. The nodes, ib. Apparent
Rotation of jupiter, 483. Jupiter's
equator nearly coincident with his orbit, ib.
Jupiter an oblate ſpheroid, 484.
Spots in mars, ib. Changes in them,
485.- His rotation in 24h. 40'.-Spots
in venus, 486. Her rotation by Caffini,
487. By Bianchini, 489.-
Moun-
An argument for
tains in venus, 490.
the earth's rotation, ib. The impulſe and
velocity of the ſtars, if they go round in 24
hours, 490. The fhape of the earth a
flatted fpheroid, from centrifugal force, 491.
Jupiter flatter by his ſwifter motion, ib.
Picart's meaſure corrected, 493. A de-
gree meaſured at Peru, 494.
A large
mountain attracts a plummet out of its per-
pendicular, 496.
Chap. 11. Spots on the fecondary planets:
their rotations: the librations of the
· moon, 496.
Moon's
Her poles, equator, her
In longitude and in lati-
Spots on fecondary planets, 496.
rotation, 497.
libration, ib.
tude, 498.
Chap. 12. The apparent motion of the
fun not equable: the natural days un-
equal: clocks fometimes fafter, fome-
times flower than the fun, 499.
Day artificial, 500. — Day natural, ib.
Hours equinoctial, 501. Unequal, ib.
Sun-dials of the ancients, ib.
Water-clocks of the ancients, ib.
A meridian teleſcope, 505.
clocks, 506. Natural days unequal,
when longeft or shorteft, 507. A table
of them, 508.Sun-dials of the ancients,
Clepfydra, 510.
509.
5 B
-To examine
Chap.
CONTENT S.
Chap. 13. Weeks, months, years, pe- Chap. 18. The tranfit of venus over the
riods, or cycles, 510.
Months, 511. Year, ib.
Jewish, Greek,
Lunar year, 513.
Weeks, ib.
514.
Intercalation, ib.
Meton's
Ju-
cycle, ib. Year Roman, 515.
lian year, 516.Year tropical, ib. -
Gregorian year, 517. Decads of the
Greeks, ib. Calends, nones, ides, 518.
Roman week eight days, 519.
Domi-
nical letter, ib. Eafter, ib. Jewish
paffover, 520.
Golden number, 523.
Epacts, ib. Epacts and golden
number in Gregorian calendar, 525.
Indiction, 534.
British calendar, 533
Julian period, 535.
Chap. 14. Epochs: araes, 536.
Chriſtian æra, 536.
Creation of the world,
537. Chaldean and Egyptian pretended
antiquity, 538.Difference between He-
brew and feptuagint, 539 Jews falfify
the date of the creation, 540. Olym-
piads, ib. Building of Rome, ib.
Nabonaffor, ib.
Chap. 15. Of comets, 542.
The greateſt velocity of a comet, 550.
Head or nucleus, ib. Of different mag-
nitudes, 552. Tails of comets, 553-
Comet of 1680, 556. Its vaft
heat, ib. Caufed the deluge, according
to Whiſton, 558.
The return of a co-
met foretold by Halley, 560. Uſe of
comets falling into the fun, 563.—Supply
water to planets, ib.
Chap. 16. Poetical rifing and ſetting of
the stars and planets: calendars or
almanacks, 563.
Cofmical, ib.
Achronychal, or heliacal,
Calendars, or diaries, 565.
English calendars abfurdly foretell weather,
Dog-ftar, 568.
Dog-ſtar, 568.———— Dog-days, ib.
564.
567.
Chap. 17. Ufe of the celestial globes, 570.
fun, June 6th, 1761: the parallax
of the fun: the atmoſphere and fatellit
of venus: the latitude of Cambridge
found by a gnomon, 575.
Parallax of the fun, 576.-Diameter of ve-
nus, 577: Her atmoſphere, 578.
Her fatellit, 580. Solftice obferved at
Cambridge, 582.Latitude of the place,
583.
BOOK IV.
Chap. 1. Natural philofophy what: its ufe:
the creation of the world, according to
ancient and modern philofophers, 585.
Natural philofophy what, p. 585.Impor-
tant uſes of it, 586. Opinions of phi-
lofophers, concerning the formation of the
univerſe, ib.- Arguments for its eternity
anſwered, ib. Ancient philofophers in
general Deifts, 587. -Defcartes Opinions,
ib. Plenum, ib.
ib.- Denied the motion
of the earth, ib. His firft elements what,
588. Mode of accounting for the for-
mation of the fun, planets, &c. and their
motions, ib.Vortices, ib.-Dr. Bur-
net's Theory, ib. Shewn to be neither
agreeable to ſcripture or found philoſophy,
by Keil and Woodward, 590. Wood-
ward's Natural Hift. of the earth, ib.
Its defign, ib. Why fea-fhells, &c. are
found on the tops of mountains, ib.
Leibnitz's opinion concerning the origen of
the earth, 591. Whifton's Theory, ib.
Halley's Theory of the Variation of the
Magnetic Needle, adopted by Whiſton, 592.
Whifton's Theory not fo exceptionable as
Burnet's, ib.-Buffon's whimsical Theory,
ib. Theſe feveral theories compared,
593.
-General error of thefe cofmogo-
nifts, 594. Plato's opinion of the for-
mation of the world, ib.
Chap. 2. The prefent conftitution of the
univerfe, according to the ancients
and moderns: the Newtonian philo-
fophy: definitions of time, space, mat-
ter and motion, 595.
Opinions of the ancients concerning the pre-
fent conftitution of the univerſe, 595.
The
CONTENT S.
1
The opinions of the moderns, ib. Phi-
lofophy brought from Egypt into Greece,
ib. Opinions of Ariftotle, 596.
Principal diſcoveries of the moderns before
Sir Ifaac Newton, 597.
Newton's me-
thod of philofophizing, ib. Laws to be
obſerved in it, ib.Time, fpace, place,
and motion, are both abfolute and relative,
598. Abfolute time what, ib. - Re-
lative ditto, ib.· Abſolute ſpace, ib.
Relative, ib. Abfolute and relative place
what, ib.- Abfolute motion, ib.-Re-
lative motion, 599. Matter defined, ib.
Quantity of matter what, 600.
Quantity of motion what, ib.Impreffed
force what, ib.Percuffion, ib.
-Cen-
tripetal force, 601. Abfolute quantity
of centripetal force, its meafure, ib.
Accelerative centripetal force, ib. Mo-
tive centripetal force, ib. Gravity what,
ib. No mechanical caufe to be affigned
for it, 602. Newton's laws of motion,
603.
Chap. 3. Gravitation: laws of falling
bodies: pendulums: projectiles: centri-
petal force: repulfion: électricity,604.
Gravitation explained and illuftrated, 604.-
The notion of gravity not new, 605.
Law of gravitation, 606. Experiments
to prove it, ib. Pendulum what, 607.
Its uſe, ib.
Mr.
Laws of it, ib.·
Graham's quickfilver pendulum, ib.
The gridiron pendulum, ib.-Lever pen-
dulum, ib. Laws of defcending bodies
difcovered by Galileo, 608. Projectile
what, ib. Defcribes a parabola in vacuo,
ib. Theory of projectiles, 609.-
Applied to the planetary motions, 610.-
The planets defcribe ellipfes, 611.-Whi-
fton's opinion on this head, 613.-
ory of the diurnal motions, ib.
effect of theſe motions on the figure of the
planets, ib. The moon impelled round
her orbit by a projectile force, and retained
in it by a centripetal force, 614.
The-
The
That
the force which retains the moon in her or-
bit is the fame with that by which a ſtone
falls to the earth was diſcovered by Newton,
ib. Proof of this propofition, ib.
Jupiter and faturn, when near the conjunc-
tion, difturb each others motion, ib.
Theſe planets probably diſturbed by the ac-
tion of comets, ib. Various phenomena
cauſed by attraction or gravitation, ib. ——
Other kinds of attraction, 615.-Repul-
fion inherent in ſome bodies, ib.—Greateſt
in the air, 616. Air contained in all
bodies, ib. Sir Ifaac Newton's Ether,
617. The Author's opinion, ib.
Electricity, 618.Writers on it, ib.
Uſes reſulting from the knowledge of it, ib.
Magnetifm, 619. Pendulum more
particularly deſcribed, ib. Whifton's
opinion, (p. 613.) cenfured, 619. Co-
mets not ſo liable to difturb the motions of
the planets, on account of the excentricity
and various fituations of their orbits, 620.
Chap.4. The irregularities of the moon's
motion caused by the attraction of
the fun, 620.
The fquares of the periodical times of bodies
revolving about a center are as the cubes of
their diſtances, 620. The attractive
force of a body is as the quantity of matter,
ib.Irregularities of the moon owing to
the action of the fun, ib. Illuftrated,
621. The form of the moon's orbit
variable, 622. Apogee and perigee of
Line of the ap-
the moon what, 623.
fides what, ib. Moon's anomaly what,
625 The place of the nodes of the lu-
nar orbit changed by the action of the fun,
626. Mean motion of the nodes retro-
grade, 627. The plane of the lunar
orbit changed by the action of the fun, 628.
The earth and moon neareſt the fun
when the earth is in perihelion, 629.
The diſturbing force of the fun is then
greateſt, ib.
The tides
Kepler the
Chap. 5. The tides, 629.
Meaning of the word, 629.
influenced by the moon, ib.
firft, who thought the waters gravitated to-
wards that planet, ib.
Demonftrated to
do fo by Sir Ifaac Newton, ib. The
nature of this influence explained, 630.
The tides influenced by the fun, 631.
Height to which they rife in the open ocean,
ib. At the Severn mouth, ib.
Greatest tides in the fyzygies, and at the
equinoxes, 632. The tides influenced
by the wind, ib. Sir I. Newton's ex-
planation of the cauſes of the tides, 633.
-
5 B 2
Chap.
CONTENT S.
Chap. 6. The precefion of the equinoxes:
the nutation of the poles, 634.
M aclaurin's explanation of the cauſe of the
preceffion, 634.
tion of it, 635.
poles explained, ib.
The Author's explana-
The nutation of the
Difcovered by Dr.
The planes of
Bradley, 636.Deſcription of Dr. Brad-
ley's inftrument, 637.
Heathcote's Hift. of Aftronomy, ib.
Efteve's Hift. of Aftronomy, ib.
judgement of Weidler's work, ib.
M. Caffini's, ib.
His
Of
De la Caille's Hift. of
Aftronomy for 30 years paft, ib.
Lande's Hiſt. of Aſtronomy, 649.
De la
The
first and last of thefe works chiefly followed.
by the author, ib.
the planetary orbits variable, 638. The Chap. 2. Aftronomy of the Antedilu-
quantity of that change calculated, 6 39.
Quantity of the preceffion variable, ib.
Obliquity of the ecliptic variable, ib.
Chap. 7. The fyftems of Ptolemy, Tycho
Brabe, &c. 640.
The Ptolemaic fyftem took its name from that
author, 740. Was received by the an-
cient Greeks, ib.-The Pythagorean fyf-
tem oppoſed by Ariftotle, ib. The Pto-
lemaic lyftem generally approved before the
time of Copernicus, ib The Ptolemaic
fyftem explained, ib. Theories of ex-
centrics and epicycles, 641. Milton's
ridicule of them, 642. Syftem of the
ancient Egyptians, ib.Of Tycho Brahe,
ib. — Tycho's reafons. for rejecting the
Copernican fyftem, 643. Kepler's doc-
trine of intelligences, ib. Paffages in
Scripture reconciled to the Copernican
ſyſtem, ib.
vians, 649.
The ſcience of aſtronomy of great antiquity,
ib. Adam probably not without fome
knowledge of it, 650. Adam's hymn
from Milton, ib. Seth an aftronomer,
according to Jofephus, 651. The au-.
thority for it contefted by Shuckford, ib.
The great length of life which the Antedi-
luvians enjoyed favourable to the ſtudy of
aftronomy, ib.Noah probably retired
into China after the flood, and carried. with
him all the knowledge of the Antediluvians,
652. The early knowledge of the grand
year of 600 common years, a proof that
aſtronomy was cultivated very early, 653.
Chap. 3. Aftronomy of fabulous times,
653.
Conjectures concerning Uranus, 653.-
Atlas, ib. Prometheus, ib. Endy-
mion, 654.
Chap. 8. Of a plurality of worlds, 644 Chap. 4. Aftronomy of the Chaldeans
Objections to the whole creation being formed
only for the benefit of man, 644: Plu-
rality of worlds embraced by feveral of the
ancients, ib. Fontinelle and Huygens
treatiſes on this fubject characterized, ib.
Comparative heat of the fun in the feveral
planets no objection to this doctrine, 645.,
-the torrid and frigid zones thought not
habitable formerly, ib. Opinions on this
head concerning the moon; ib.-Lengths
of the days in the feveral planets no objec-
tion to their being inhabited, 646.
Theſe ſpeculations not of much confequence
to us, ib. Milton's reproof of them
juſt, ib.
BOOK V.
Chap. 1. Introduction to the Hiftory of
Aftronomy, 647.
Weidler's Hift. of Aftronomy, ib.-Coftard's
Letters to Martin Folkes, Efq; 648.
and Egyptians, 654.
The Greeks wrote firft on aftronomy, 654.
Not the first cultivators of it, ib.
Uncertain whether the Chaldeans or Egyp-
tians first cultivated it, ib. Both nations
pretend to an extravagant antiquity in the
knowledge of it, ib. Obfervations found
at Babylon almoſt as early as the flood, ib.
Authorities for the antiquity and accuracy
of the Chaldean aftronomy, 655.- The
Chaldeans obferved eclipfes 720 years before
Chrift, 655.- Tower of Belus defcribed,
656. The Chaldeans formed ſeveral of
the conftellations, ib. Knew the length
of the folar year, ib. Obſerved comets,
ib.
Greatly addicted to aftrology, 657.
Character of Montucla's Hift. des Ma-
themat. ib. Length of the fydereal year
according to the Chaldeans, ib. — Dial-
ling known amongſt them, ib.
Dial of
Ahaz, 658 -The Egyptians as early in
their
CONTENT
S.
their ſtudy of aſtronomy as the Chaldeans,
ib.The pofition of the pyramids a proof
of it, ib.Had.obferved 1205 eclipfes be-
fore the time of Alexander the great, ib.
Had obfervations of the ftars 1500
years before Chrift, ib. Their firft know-
ledge in astronomy afcribed to Sefoftris, ib.
They had meaſured the magnitude of
the earth, 659. Syftem of the world em-
braced by them, ib. Length of the year,
according to them, ib. Their fothic
year, 660. Circle of Ofymandyas, ib.
The Egyptians fond of aſtrology, ib.
Chap 5. Aftronomy of the Chineſe, and
other orientals, 661.
Claims of the Chineſe to an early knowledge
in aftronomy, 661.- Noah contempo-
rary with, and probably the fame perfon
with Fohi, ib. Yao, the fixth emperor
from Fohi, taught them aſtronomy, and the
length of the year, ib. Date of the Chi-
neſe chronology, ib. The Chineſe ſigns
of the zodiac, 662. The names of their
conftellations, ib. Form of their con-
ftellations, 663. Skill in predicting eclip-
fes, ib.
Their early obfervations of them,
664. Remarkable uſe made of one of
them, ib.
The truth of their obferva-
tions to be fufpected, 665. — Claim the
invention of the mariners compaſs, ib.
Obferved meridian attitudes by the gnomon,
666. Had Treatifes on Aftronomy,
which were written 200 years before Chrift,
ib. Tcheou-cong, a celebrated Chineſe
aftronomer, lived 1000 years before Chrift,
ib. Their tribunal for aftronomy, ib.
Bonzes, or the diſciples of Fo, ib.
They hold the doctrine of metemſychofis,
667. Low ftate of aftronomy amongst
the Chineſe at prefent, ib. Its caufes,
ib. General learning of the Chineſe,
668: What it confiſts in, ib. The
proper motion of the ftars known to them
284 years after Chrift, ib. Its quantity
according to them, ib. Aftronomy of
>
the Siamese, 669. - Sphere of the In-
dians, ib.
Chap. 6. Aftronomy of the ancient Greeks
before the foundation of the Alexan-
drian School, 669.
The Greek aftronomy not ſo ancient as that
of the Chaldeans and Egyptians, 669.-
The forming of the ftars into conftellations
referred by Sir I. Newton to the time of the
Argonautic expedition, ib. Time when
Hefiod flourished, 670.- Thales travelled
into Egypt, ib.Determined the height
of the pyramids, ib. Flourished about
The first
615 years before Chriſt, 671. -
who predicted a folar eclipie, ib.-Form-
ed the conſtellation of the leffer bear, ib.
-Meaſured the fun's diameter, 672.-
Obferved the folftices, ib. Obferved
eclipíes, ib. — Anaximander invented, or
introduced the ufe of the gnomon into
Greece, ib. Made a fun-dial, ib.
Made the first globe, ib, Pherecydes
taught the uſe of the pole and gnomon, ib.
Anaxagoras predicted an eclipfe of the
Pythagoras travelled into Egypt,
Became the head of the Italian
Held the earth to be a globe,
ib. That the fun was in the center of
the mundane ſyſtem, ib. And that the
planet venus was both the evening and
morning ftar, ib. Philolaus firſt taught
that the earth moved in an orbit round the
fun, 674. ———— Meton formed the lunar cycle
of 19 years, ib. Aftronomy under little
obligation to the academics and peripatetics,
ib.Ariftotle cenfured, ib. Eudoxus
first applied geometry to aftronomy, 675.
fun, ib.
673.-
fect, ib.
Studied in Egypt, ib.Infifted
ftrongly on the neceffity of making obſerva-
tions, ib. Corrected the length of the
year, by adding 6 hours to it, ib. Verfed
in the doctrine of projections, ib. — Did
not form his fphere from his own obferva-
tions, ib. Calippus formed his period
of 76 years about 340 years before Chrift,
ib. The Greeks migrate into Egypt
and Europe, and carry the Pythagorean fyf-
them with them, ib.—The ancient Druids
ſkilful in aftronomy, 676. Pytheas of
Marſeilles, ib. The Greeks owed their
knowledge in aftronomy to the Chaldeans
and Egyptians, ib.
Chap. 7. Aftronomy of the Greeks after
the foundation of the Alexandrian
School, 677.
Foundation of the Alexandrian ſchool by Pto-
lemy Philadelphus, 677. Timocharis
and Aryftillus the firft obfervers there, ib.
Aratus the aftronomical poet, 678.
Ariftarchus of Samos an affertor of the
Pytha-
CONTENT
S.
Pythagorean fyftem, ib. Eratofthenes
invited from Athens to Aleaxandria, ib.
Meaſured the magnitude of the earth, ib.
Berofus brought many things relating to
aftronomy from Babylon, ib. Archi-
medes the greatest mathematician and aftro-
nomer amongst the ancients, 679.- De-
termined the dimenfions of the mundane
fyftem, ib. Made aftronomical obferva-
tions, ib.
The manner of his death, ib.
Hipparchus obferves at Rhodes, ib.
Difcovered the orbits of the planets to be
eccentric, 680. The motion of the
moon's nodes, and the preceffion of the
equinoxes, ib. Attempted to meaſure
the diftance of the fun from the earth geo-
metrically, ib. Failed from a defect in
Formed a cata-
the obſervations, ib.
logue of the fixed ſtars, ib. Calculated
the eclipfes for 600 years, 681.
Mene-
laus compofed 3 books of fpherics, ib. -
Made aftronomical obfervations at Rhodes,
ib. Agrippa obferved the conjunction
Theon
of the moon and pleiades, ib.
of Smyrna obferved the greateft latitude of
venus, ib. Ptolemy the firſt aſtronomer
whoſe works are come down to us, ib.
Wrote the Almageft, ib.
erroneous, ib.
His fyftem
The divifion of his Al-
mageſt, 682. That work tranſlated into
Arabic and Latin, ib.
Chap. 8. Aftronomy of the Arabians,
Perfians, and Tartars, 683.
The
Europe funk in barbarifm from the 8th to the
14th century, 683. Formation of the
Arabian empire, ib.A tafte for the ſtudy
of aftronomy introduced amongst the Arabs
by Almanzor, the 2d caliph, ib.
caliph Almamon cultivates aftronomy, ib.
Stipulates with Michael II. for leave to
fearch Greece for books of fcience, ib.
Determines the obliquity of the ecliptic, ib.
Meaſures a degree of the earth, ib.
Alferganus wrote Elements of Aſtronomy,
684. Albategnius made obfervations at
Antioch, ib.Conftructed aftronomical
tables, ib. Diſcovered the motion of the
fun's apogee, ib. Obferved the quantity
of the preceffion of the equinoxes to be a
degree in 70 years, ib.- Ebn Younis ob-
ferved eclipfes at Cahir, ib. - Naffir-Ed-
din-Ettufi obferves at Maraga, ib.
Constructs the Tabule Ilchanicæ, ib.
Ebenfophi and Arzachel, Almeon and The-
bet-ben-chora make aftronomical obſerva-
tions, 685. Alhazon wrote a treatiſe of
optics, ib.Ulug Beigh grandſon to Ta-
merlane, ib. Had a quadrant of 180
feet radius, ib.- Compofed aftronomical
tables for the meridian of Samarchand, ib.
Made a catalogue of the fixed ftars, ib.
We owe the prefent form of our trigo-
nometry to the Arabians, ib.-The Ara-
bians had the ten digits from the Indians,
686. Arzakel author of the Toledo
tables, ib.The Arabians brought afro-
nomy into Europe, ib.
Chap. 9. Of the restoration of aftronomy
in Europe, and its progress from 1230
to 1560, 686.
The emperor Frederic II. began to restore
learning in Europe, 686. Cauſed many
learned works of the ancients to be tranſlat-
ed, ib. John de Sacrobofco the first ori-
ginal writer on aftronomy after the reftora-
tion of that ſcience in Europe, ib. - Al-
phonfus X. conftructed new aftronomical
tables, 687. Roger Bacon taught the
properties of lenſes at Oxford, ib.
tellio, a Polander, wrote on optics, ib.
Profatius a Jewish aftronomer, ib. Pur-
bach revived aftronomy, ib.
Publiſhed
Vi-
a Latin commentary on the Almageſt, as
tranſlated from the Arabic, ib.
Wrote
on, and made fun-dials, 688.Muller of
Monteregio, or Regiomontanus flouriſhed,
ib. Poiſoned, as is fuppofed, by the fons
of Trapezuntius, ib. Bernard Walther
practiſes aftronomy, 689. Made ufe of
clocks, ib. John Werner flourished, ib.
Obferved the motion of a comet in
1500, ib. Wrote many books on aftro-
nomy and geometry, 690. Obferved the
preceffion of the equinoxes to be 70′ in 100
years, ib.
Was the first who propoſed
the method of finding the longitude at fea,
by obferving the moon's diſtance from the
fun and ftars, ib. James Faber wrote
on aftronomy, 691.
Dom. Maria prac-
tiſed aſtronomy, ib. Copernicus flouriſh-
ed, ib. Obſerves the defect of the Pto-
lemaic fyftem, 692. Grows diffatisfied
with it, ib. Examines all the ancient
ſyſtems, particularly thoſe of Capella and
Apollonius Pergeus, ib. Approves of
that of Pythagoras, 693.
Refolves to
make
1
CONTENTS.
make tables on that hypothefis, and for that
purpoſe undertakes to make obfervations,
694.
Divifion of his work, 695.
Death, 696.John Schoner ftudies aftro-
nomy, ib.
Makes many aftronomical
oblervations, ib Peter Nonius made
aſtronomical obfer ations, 697.His me-
thod of dividing inftruments, ib.
Wrote
on the nature and cauſe of the twilight, ib.
On navigation, ib. Shews the errors of
Orontius, ib.Peter Appian ftudies aftro.
nomy, 698. Dedicates his Cefa, ean
Aftronomy to Charles V. ib.- Obferved
many comets, ib The first who re-
marked that their tails were always turned
from the fun, ib. - Rheticus Alouriſhes,
ib. Computes tables of natural fines
and tangents, &c. to every 10th ſecond, ib.
Gemma Fufius applies himself to the
ftudy of the mathematics, 699. Was
the first who recommended a time-keeper
for determining the longitude at ſea, ib.
Chap. 10. Of the improvements in aftro-
nomy before the invention of teleſcopes.
William Landgrave of Hefs cultivates aftrono-
my, 700.- Affifted by Chriſt. Rothman
and Juftus Burgius, ib. Formed a ca-
talogue of the fixed ftars, ib. - Tycho
Brahe born at Knudftrop, ib.Is fent to
Leipfic, ib. Studies aftronomy, ib.
Obferved the new ſtar in Cafiopea's chair,
701. Made a new catalogue of the fixed
ftars, ib.- Recommended by the Land-
grave of Heffe to Frederic II. K. of Den-
mark, ib.Builds the obfervatory at Ura-
niburg, 702. Account of that Atructure,
ib.
The inftruments it contained, ib.
Diagonal divifions invented by Richard
Chancellor, ib.- Thefe divifions not accu-
rate, ib. Corrected by Ferrarius, ib.
Tycho careffed by perfons of the higheſt
rank, ib. Envyed on this account, ib.
The death of his patron, ib.
His
misfortunes in confequence of it, ib.
Entertained by the emperor Rodolphus, 703.
The inventor of a new ſyſtem, ib.
His death, ib.Longomontanus affifted
Tycho Brahe, 704. Said to have known
the uſe of logarithms before Neper, ib.
Kepler's particular turn for fpeculative aftro-
nomy, ib. Becomes acquainted with.
Tycho Brahe, ib. Difcovered the orbits.
of the planets to be elliptical, 705.-That
the fquares of their periodic times are as the
cubes of their diftances from the fun, ib.
-Had fome notions of the principle of
gravitation, ib. His writings, ib. -
Edward Wright difcovered the true princi-
ples of constructing ftraight lined charts,
706. Lord Neper invents logarithms,
ib.-Logarithms improved and calculated
by Briggs, ib.Cultivated by Gellibrand,
Gunter, Urfinus, Vlacq, &c. ib. John
Bayer publiſhes his Uranometria, ib. —Öther
cultivators of aftronomy in this period, ib.
Chap. 11. The history of aftronomy from
the invention of teleſcopes to the end
of the 17th century, p. 707.
Roger Bacon probably first acquainted with
the effects of a combination of optic glaffes,
707.
Contended for by Alexander de
Spina, ib. Teleſcopes firft actually con-
ftructed by Zachary Johannides, ib.
Claimed by John Lipperhoy, ib Gali-
leo re-invented them, ib. Diſcovered the
irregularities in the moon's furface, 708.
—
That venus put on the fame phaſes
which the moon does, ib. Jupiter's fatel-
lits, and faturn's ring, ib. Difcovered
the ſpots in the fun, and its revolution on
its axis, 709.-
The caufe of the via lactea,
ib. The nature of nebuloſe ſtars, ib.
He propoſes to make use of the fatellits of
jupiter for finding the longitudes of places, ib.
M. de Peirefc applies to the theory of
thefe fatellits, ib. M. Morin's methods.
of finding the longitude, ib. Galileo's
treaty with the Dutch for finding the lon-
gitude at fea, ib. Reineri's Medicean
tables, ib. Gave no tables for the fatel-
lits, 710. Hodiorna's tables and thofe of
Marius for the fatellits of no uſe, ib.
Caffini's fuccefs in this buſineſs, ib.
Progreſs made by Urfinus, Briggs and Vlacq,
in the calculation of logarithms, 711.-
Gardiner's edit. of Logarithmic Tables, ib.
Horrox, by his own obfervations, corrects
the theory of Venus's motion, ib. Dif-
covered that this planet would paſs over the
fun's disk in 1639. His and Crabtree's
obfervation of it, 712.
Foundation of
the Royal Society, ib. Of the Royal
Academy of Sciences at Paris, ib. Heve-
lius-His obfervatory and inftruments, ib.-
Works, ib. His difpute with Hook, it,
Halley deputed by the Royal Society to en-
ib.
quire
CONTENT S.
quire into the merits of it, ib. His man-
ner of obferving, 713.
tory built at Paris, ib.
ib.
ib.
ib.
ib.
Royal Obferva-
At Greenwich,
Fontana improves teleſcopes, 714.
Huygens makes very long ones, ib.
Difcovers the fourth fatellit of faturn,
Applies pendulums to clocks, ib.
Campani improves teleſcopes, ib. -
Caffini diſcovers all the fatellits of faturn,
Gaſcoigne invents the micrometer,
M. Auzout re-invents it, ib.
The reflecting teleſcope firft mentioned by
Merfennus, 715. —
Gregory fhews the
method of conftructing one, ib. Two
executed by Newton, ih. Caflini placed
in the Royal Obfervatory at Paris, 716.-
Drew the meridian line in St. Peter's church
at Bologna, ib. Flamsted eſtabliſhed at
Greenwich, ib. Great merit and affi-
duity as an obſerver, ib.
catalogue of the ſtars, ib.
astronomical tables, ib.
Forms a new
Conftructs
Roëmer difco-
vers the progreffive motion of light, ib.
His Triduum Roëmerianum, 717.
Chap. 12. The hiftory of aftronomy fince
the commencement of the preſent cen-
tury, 717.
Practical aftronomy languiſhes for want of in-
ftruments, 717.-Newton publiſhes his
Principia, ib. Neglected by foreigners,
718. Underſtood and ftudied at home,
ib. Embraced fuddenly abroad, ib.-
His philofophy not fubject to change, ib.
1
Improvements in inftruments firft be-
gun in England, ib. Still fuperior to all
other nations in this refpect, ib. — Gra-
ham's excellency in conftructing them, ib.
Dr. Bradley diſcovers the aberration of the
fixed ſtars, ib. Hooke's obſervations
Halley's eminence in
aftronomy, ib. His voyage to St. He-
lena, ib. The firft who predicted the
return of a comet, ib. Shewed the im-
portance of obſervations of venus's tramfits
over the fun's disk, ib.Compoſed aftro-
erroneous, 719.
nomical tables, ib.
fervations, 720.
ib.
His numerous ob-
Death, ib.
Dif-
Made
His
pute concerning the figure of the earth, ib.
Two degrees meaſured to determine-it,
The refult, ib. Bougeur and
Condamine obferve the attraction of moun-
tains, 721.—The reflecting teleſcope im-
proved by Hadley, ib. Invents the re-
flecting quadrant, ib. Newton had
thought of it before him, ib. Dr. Brad-
ley fucceeds Halley at Greenwich, ib.
The accuracy of his obfervations, ib.
Improved the lunar tables, ib.
tables of the fatellits of jupiter, ib.
tables and rules for the refractions, ib.
Procured better inftruments for the obſer-
vatory, 722. The progrefs made in re-
ducing Newton's theory of the moon to
practice, ib.The merits of the different
tables deduced from it, ib. Mayer's re-
ward from the board of longitude, ib.
Wargentin's tables of the fatellites, 723.
The excellence of Bird's inftruments,
Of Short's reflecting teleſcope, ib.
The divided object-glaſs micrometer,
Dollond's improvements of the re-
fracting teleſcope, ib. Improvements
made in aftronomy abroad, 724. La
Caille's voyage to the Cape to obſerve the
lunar parallax, ib. Re-examines the
places of the fouthern ſtars, ib. Mea-
fures a degree of the meridian there, ib.
Obfervation of the tranfit of venus in 1761,
ib. Death of Dr. Bradley, 725.
Succeeded at Oxford by Mr. Hornby, ib.
ib.
ib.
·
₹
At Greenwich by Mr. Blifs, ib.
Dr. Maſkelyne appointed to the Royal Ob-
fervatory at Greenwich, ib. His fuccefs
in bringing the lunar method of dilcovering
the longitude into practice, ib.
The
importance of aftronomy, ib.The an-
cients opinion of the Deity, ib. The
abfurdity of it, ib. The power of God
moft manifeft in the Heavens, 726.
Capella not the inventor of the fyftem which
is fometimes afcribed to him, ib.-Names
of the Deity, 727. Derived from his
different operations and relations to us, ib.
Conclufion, 728.
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